Here's the former Mayor of New York receiving the Legion d'honneur from President Mitterrand, here's another distinguished-service gong being pinned on by Carl Gustav of Sweden. Here's a warm handshake with Anwar Sadat, a triptych of encounters with Mother Teresa, a meet-and-greet with the Pope. Across the end wall is a dramatic photograph of scores of framed portraits mounted onto a metal scaffolding on Ellis Island: "They're pictures by Fred Brennan of 40 Jewish people who've had a major impact on American life," says Koch neutrally. "Everybody could pose just the way they wanted. Look, there's Kissinger, and Ralph Lauren, and Steven Spielberg and Arthur Sulzberger hiding his face, and, er, Allen Ginsberg..." When I don't immediately pick him out, he volunteers, "That's me over there", and we look at the photo of Koch in shirtsleeves, leaning out of the frame with thumbs aloft, filling the available space.
The man known in America as "Hizzoner" (as if in amazement that such a rough diamond, of Polish-Jewish rag-trade stock, should have reached high office) wears his celebrity lightly. Some years after he stood for an unprecedented fourth term at City Hall, and lost to David Dinkins, he is as busy as ever, advising, commentating, evaluating and discharging views with the ballistic energy of a Heckler & Koch (a relation?) assault rifle. "Yeah there's life after being mayor," he says with a slight defensiveness. "Want me to spell it out? I'm a partner in this law firm. I do a radio show every day from this office [he jerked a thumb at the microphone and headset behind his chair]. I have two television shows. I'm writing my tenth book. I do commercials. I speak around the country. I do movie reviews in six newspapers every week. I did a political column in the New York Post until we had a difference of opinion and I quit, but I'll probably get another such column..." Bit quiet for a man of 72, I observed. You must find time hanging rather heavy... "I enjoy it all," said Koch firmly. "I like being relevant."
His relevance today for New Yorkers is as an elder of the tribe, a seasoned and weathered piece of reliable furniture in the living room of the American consciousness, a moral lodestone for a confused, millennial generation. In the 12 years that he ran New York, balancing its precarious accounts, healing racial wounds, repairing the pock-marked streets and presiding over a boom on Wall Street, he convinced the 7 million-strong urban population that he was the one incorruptible politician they'd ever known. With his constant catchphrase of "How'm I doin'?" he demanded approval for every initiative, from providing low-cost housing to making sure schoolchildren didn't say "ax" when they meant "ask". A natural media presence, he turned up on television as guest host of Saturday Night Live, walked in street processions wearing silly clothes, and became the most high-profile senior American politician outside Washington.
His current relevance to British people, however, is considerable. Next month, the government White Paper on the administration of London will be published, while in May a referendum will establish whether the nation fancies the idea of a directly-elected executive mayor running the metropolis. If the results are favourable, London will get its own version of Ed Koch, with powers over the police, the judiciary, the people responsible for housing and education and urban planning. And then - who knows? - a proper, American-style mayor of Bristol, of Manchester and Birmingham. Why, there might even be one of Weston-super-Mare.
"You must remember there's a whole range of mayoralties in America," said Koch. "from weak to strong. In the weakest, everyone is elected to a board, and they rotate the mayoralty within it. But the decisions are all made by the commission of seven people, and the title's merely honorific. There's another kind, where the mayor appoints a city manager but once he's in place he runs the city and can't be removed and the mayor just cuts all the ribbons."
And the Koch kind? "In New York City we've a strong mayoralty, the best kind, where the mayor is chief executive and has executive powers, who appoints the city commissioners and the judges, whose signature is required to sign the budget or veto it, and who runs the city through administering different agencies." He rubbed his chin. "When I was mayor - and I think I was a pretty good mayor - I appointed people with special skills in operations and policy planning and economic development and the capital budget - and they were all wonderful." I said that, as things stand, the new-look London mayor would have his or her powers severely clipped by a proposed "Greater London Assembly", which would be free to alter the mayor's proposed budget as it liked, and whose collective decisions could not be vetoed by mayoral diktat. "Is that so?" asked Koch with distaste. "The mayor of London can't veto assembly decisions? So what do they need a mayor for?"
I thought of the paddock of mayoral hopefuls who have neighed and snorted at the starting gate since the idea was first mooted - Ken Livingstone, Jeffrey Archer, Tony Banks, Simon Jenkins, Richard Branson, Chris Patten - and of how they would love the no-strings autocracy of the New York model, and how nervous it would make a lot of people in the Palace of Westminster. The heady mixture of civic autocracy and national renown can very easily go to the heads of backbenchers and politicians who have never quite made the cabinet. No wonder Jeffrey Archer told the editor of the Times that his long-range bid to be London's executive mayor was "the biggest, most important political campaign of my life".
"Who is this Archer guy?" asked Koch. "Some kind of television personality?"
No, no, I replied. He's the former deputy chairman of the Conservative Party and a peer of the -
"Right," said Koch, absently.
Had Koch's fame, his constituency of 7 million supportive citizens, ever made him a figure to rival the President? "I never thought of myself in the same class as the President of the United States," he said, sounding shocked (and respectfully using the full title, just as he always says "New York City" rather than "New York"), "I was merely his humble servant." He got on, he says, with all the inhabitants of the Oval Office, before it became the Oral Office. "I got on best with Reagan, who I thought was very effective and very decent." But weren't their views wildly divergent? Koch, after all, started out on the Sixties liberal-left, protesting against the Vietnam war, keen on the legalisation of marijuana. More recently he's called himself a "liberal with sanity". Whereas Reagan... "He was a very conservative Republican," said Koch, "while my views were those of a moderate Democrat. I didn't agree with him on a host of issues, but I liked him personally and he liked me, and that goes a long way. And I helped move my party closer to the centre."
Just to check, I asked, what kind of platform of beliefs does a moderate Democrat promote these days? "I'm in favour of school vouchers," he said airily, "and the death penalty, and..." Hang on, I said, since when was that a moderate view? "Sure it is. I think of the death penalty as a liberal position. If you believe in the rights of society as being paramount, then you wanna protect society. That's liberal. I'm for the death penalty. I think it protects society."
But, I protested, if that's moderate, what would a right-wing position favour? Flaying people alive? "You're thinking of the punishment. I'm thinking of what's in the interests of society. Okay, most people don't agree with me, but what do I care?"
He smiled, his battered-cherub face creased with pugnacious amusement. You can write off Koch as a crypto-redneck at such moments, or be appalled by his hawkish view of current affairs ("I hope they do bomb Saddam, but the longer they take, the fewer are the chances of them actually doing it. Sure, I'm looking forward to it. I'm for bombing him back to the Stone Age"). But it's fascinating to see how he turns ideas into action, and how he used the office of mayor to pursue a private agenda in small and large things.
City councils outside the trendy purlieus of Lambeth are not known, by and large, for making pronouncements on foreign policy; but Koch has never been shy of intervening in issues well outside his backyard, or of putting pressure on regimes of which he disapproves. He has abused the Russian government (which he calls "the pits"), taken a Westminster line on Ulster, commented on West Bank negotiations, had a poke at Tokyo. "Every mayor indulges in foreign policy in a figurative sense," he says. "You can follow your impulses because the city's budget buys so much. When I was mayor, the city of New York made purchases of goods and services worth $15bn every year. So we could say, We won't buy from any country that does this or that thing. We said in the past, we won't buy from companies that sell to South Africa. We had legislation that was stronger than the federal governments on companies that boycotted Israel.We said, if you boycott Israel, then you can't sell to us..."
He has, he confesses, done occasional things to the city on pure personal whim. "You know the intersection of 42nd Street and Twelfth Avenue, right where the Chinese Mission is? I changed it to `Tiananmen Square Corner'. I intended it," he concluded gratuitously, "to be provocative." And when visiting China, whose regime he denounced while still being shown around Beijing by his hosts, he had a brainwave. "I noticed that at five o'clock, a million people got on their bikes and rode home. I thought, Gee, wouldn't it be nice to have people ride bikes in New York City and get rid of the cars? So I called in the commissioner of transportation and said, I wanna put a bike lane up Sixth Avenue and down Seventh - how much and how long? He came back and said, `It'll cost $3m and take six months'. I said, Lemme explain something, If you aren't able vastly to change both those figures you won't be commissioner much longer. He reconsidered and said, `We can do it for $300,000 and it'll take six weeks.' So we did. I went out and looked to see if the bikers were using their special lanes, and they weren't. They preferred the traffic and risking their lives, you know how people are. So I put up a sign saying `Bikers - Use 'em or lose 'em. You've got 30 days.' And I checked and they still weren't using them so I took 'em all down in 48 hours."
A more substantial achievement was to rebuild the Bronx, New York City's most run-down district, over a decade, using $5bn of city (rather than federal) money to rehabilitate the abandoned buildings. Koch cannot walk down the Grand Concourse in the Bronx today without a warm feeling of having made a difference. But then tales of civic heroism are meat and drink to him. He has, you suspect, a sentimental streak a mile wide under his bracingly tough exterior. He clearly relishes the role of modern-day TV Solomon on The People's Court, where members of the public bring their grievances and solicit his judgement (which is legally binding, with no appeal). Some of the cases are idiotic (such as that of Ms Flossie Torgerson, a 74-year-old LA pensioner whose pet chihuahua Babette was eaten, or at least swallowed, by a 7ft boa constrictor belonging to a young headbanger living next door) but most are everyday stories of greed and malice and bad behaviour. Mr Koch believes in upholding the law rather than demonstrating his compassionate nature, but he has an unusual perspective on the televising of court cases. "A courtroom can be an educational experience for the public, but it also means that those who participate know the world is watching them. I'm all for opening up the family court where juveniles are tried - I think we provide too much protection for them, in not revealing their names. A lot of people, particularly juveniles, ought not to be in jail, but they ought to know that their neighbours think they're shits."
Mr Koch's final word on the subject of mayors was in the same moralistic vein. I asked about the current incumbent of City Hall and Gracie Mansion (the mayoral Number Ten). "Giuliani? He's a good mayor but not a nice person. Frankly he's cruel. He goes for the jugular. If you criticise him, you're his enemy." And the last one, David Dinkins? "Nice person, terrible mayor." Wasn't it better to be effective than to be nice? "It's much better to be able to walk around the streets and have people take pride in you and what you stand for." So what kind of person do you have to be? "A mayor has to be sensitive over the needs of others. But he's also gotta be tough. But it's the way you do it, the way you come across. You can't think you're the one with the Holy Grail. All you can say is, `Listen, people elected me, and I'm gonna do what I think is the right thing, and then you'll have a chance to throw me out.' As opposed to saying, `You don't agree with me? You must be the devil incarnate.'"
Nice but tough, capricious but solid, provocative but caring. Voila the modern mayor. Got that, Ken and Jeffrey and Tony and Simon?