Bremner was flabbergasted and, no doubt, flattered by it. "I thought, 'What's going on here?'," he laughs, "they're outdoing me." Next thing we know, Mr Major will be attempting to tell jokes and usurp Bremner completely.
It is nevertheless a tribute to Bremner's uncanny accuracy that the Prime Minister should have chosen to use that particular phrase. The impressionist hits the target with alarming regularity; he is the Alan Shearer of comedy.
Part of it is attributable to a God-given gift for mimicry. "It comes down to a skill that you can't analyse," reckons Geoff Atkinson, his long- term producer on both BBC2's Rory Bremner and C4's Rory Bremner... Who Else?. "It's the same with every good performer - it looks deceptively simple. He has a coordination between eye, mouth and brain which allows him to capture people. In the office, he'll meet someone and be able to do them immediately. He doesn't take four weeks with a tape and lots of brow-beating. Like a cartoonist, you're born with it."
More than that, though, Bremner has a nose for comic incongruity; he can make such unexpected leaps as the idea of Peter O'Sullevan commentating on the BSE crisis - "and Scrag End's a faller". "That's where the inspiration starts - and, some would say, finishes," Bremner affirms. "I was watching Des Lynam last year and noticed that his hair was getting very flamboyant and showbizzy. Logically, that ends with Dessie La Rue singing 'On Graham Kelly's Doorstep'." Bremner then helpfully - and energetically - runs through the meisterwerk in a private command performance for me.
Barely pausing for breath, he continues: "If I was telling you in a nutshell what I do, I'd say I'm like a barrister. I read up on a subject for two days and then find an analogy. So the Northern Ireland peace process becomes two people trying to get a piano upstairs." Again, without prompting, he breaks into song with a version of "Right, Said Fred": "Right, said John/ Gives a shout to Paisley/ Up comes Paisley/ Tries to run the show."
This approach has helped to rehabilitate impressionism; thanks to Bremner, it is no longer a terminally passe activity practised only by men in spangly suits on ends of piers doing "Ooo, Betty" Frank Spencer impersonations. "Rory has tried to avoid being just an impressionist," Atkinson avers. "He's got something to say as well. He's playing characters, in the same way that David Jason plays Frost or Del Boy. Rory's characters just happen to be impression-based. Impressionists have never gone away, but he's helped to move the world of impressionists on. It's now no longer enough just to do the voice and the look."
Comedy being the pathologically back-biting business that it is, though, Bremner's back is not unscathed by toothmarks. The chief gripe is that Rory Bremner... Who Else? is too political. "I'm fairly thin-skinned about critics," he admits. "Because I take the homework seriously, it is perceived as a serious show about politics. People say it's tight- arsed. But there is so much more in there - I do Clive James with Eric Cantona, for instance. Anyone who watches it would see that there is a lot of celebration. The agenda is to put my finger on the truth behind politics, but it is possible to do that and entertain at the same time."
Atkinson takes up the point. "We have a dilemma. You sense that an audience can tire of politics, but the danger is that you pander to that and give them something empty of comment. You can see that even with the political parties, who prefer to argue over the Royal Yacht than Europe or the NHS. The depoliticising of society is a dangerous process. If we're not careful, we won't have debate anymore. We don't want to become pious or worthy or bleeding-heart liberal - you've still got to be funny. But comedy should not be thought of as an alternative to political comment; the two can go together. Good satire is the comedy of the truth."
Bremner will be putting this to the test in front of a live audience this spring as he undertakes his first tour for some years. He is relishing the prospect of "rediscovering the essential joy of carrying around a lot of voices in your head - you can do Camilla Parker-Bowles one minute, and Gerry Adams the next".
The tour will also afford him the opportunity "to escape from newspapers saying to me, 'What are you doing in your private life?' Nine months ago, I decided to say nothing to the papers, so they just started making things up about me. There's now a virtual-reality Rory. People ask me what I've been up to, and I say, 'I don't know, I haven't read the papers'. We've got to the stage now where Trevor McDonald will introduce the news by saying, 'Good evening, here is the gossip'."
For all that, Bremner remains resolutely upbeat. Dazzling you with more voices than the Tower of Babel, he makes for rattling good company. He is also sensible enough to know the limits of his art. "People have said they have got their political education from watching me and Spitting Image," he muses, "but I wouldn't make grand claims. The ideal thing is that at the end of a sketch people turn to each other and say, 'I didn't know that was happening'. I did a sketch about privatisation with Brucie doing The Price is Right. At the end, people might have realised that pounds 30bn was wasted. You can draw people's attention to things, but there's a strong feeling that in the ballot-box they're more influenced by income- tax policy than a comedy sketch."
Rory Bremner, Neptune Theatre, Liverpool (0151-709 7844) tonight, tour to 20 Mar
1961: Born in Edinburgh.
Late 1970s: After leaving Northside Secondary Modern, trained as an electrician, but was passionate about amateur dramatics
Early 1980s: Like countless other comedians, broke into radio on Week Ending
1985: Top 20 single with "19" about the Vietnam War
1986-92: "Rory Bremner" on BBC2
1987: Montreux Festival Press Prize
1990s: Various presenting jobs: Without Walls: J'Accuse - Dame Edna; Late Show discussion on sculptor Ronald Rae; and Scott of the Arms Antics
1992 & 95: British Comedy Awards Top Male Performer
1993: First straight role as cricketer Kevin Beeseley (Bremner himself is a keen player and spectator) in You, Me and It on ITV
1993-96: Rory Bremner... Who Else? on C4
1994: Bafta & RTS Best Light Entertainment AwardsReuse content