He gives us a lightning tour of this light, airy, largely 16th-century and quintessentially English country house, first presented to Lloyd George for his use in 1921. We see the Hawtrey room, where Churchill made some of his most famous wartime broadcasts. We sneak a look at a Constable landscape, a Reynolds portrait.
He points out 0Cromwell's muskets and Napoleon's table in the long library on the first floor, musty from the smell of old books, its curved mullioned windows looking out on the rolling Buckinghamshire countryside. Of the two official homes it is the one Tony Blairlikes, a place where he can think, a refuge for his young family from the official bustle and unhomely formality of living "over the shop" in Downing Street. The five-aside goal on the ample lawn testifies to the regular weekend presence of the Blair children.
But he isn't here to relax today. He's here to write a speech which is perhaps the most difficult of his premiership. We are right in the heart, just now, of what Mr Blair has called the "post-euophoria, pre- delivery phase" of his first term.
The latest poll shows the Government still at gravity-defying levels of popularity despite growing public pessimism about the economy. But the party is edgy; about job losses, about the charges of cronyisim the Drapergate affair brought in its wake, about the pain which may attend the difficult welfare reforms ahead. Mr Blair expects to see at least two - and perhaps more - left-wingers elected on to the National Executive this week, which will be widely read as a rebuke for the leadership from the party members.
He knows the importance of the speech in Blackpool. It will no doubt seek to reconnect the leader with his party, the head with the body. But here on the sunlit terrace at Chequers, what is absolutely clear is that he has not the slightest intention of compromising with his critics on the substance of what New Labour is about.
He positively relishes, it seems, the opportunity the widespread anxieties give him to spell out his economic message: "Domestically, the single most important thing is to produce long-term stability. The long term was never won by a faint heart, I'm afraid."
First, he says, "a sense of perspective would be a good thing. Our economy is still growing. We must be careful not to talk ourselves into a worse position than any objective assessment merits."
Yes you cannot remain immune from a world 40 per cent of which is in recession. But overall, Mr Blair points out, unemployment has fallen by 300,000 while employment grew by 400,000. Yes, the siren calls to change economic course, will "test the mettle" of the Government as they did previous governments. The difference is that this one won't change course as they did.
"We are doing something very different from previous Labour governments or even previous Conservative governments. In the first two years, we have imposed the toughest fiscal tightening for decades, given independence to the Bank of England and established a new set of fiscal rules."
The course being urged on him by William Hague was that which had led, under the Tories from the late Eighties to15 per cent interest rates, high inflation and record bankruptcies and reposessions.
Because the economic circumstances had been different people hadn't believed Mr Blair when he had said at the time that Bank of England independence was "a very bold move". He went on: "There is a political risk for the Government, but there is no doubt in my mind that we have done the right thing.
"The absolute precondition of a successful modern economy is monetary and fiscal discipline. If that is absent, you won't get a successful modern economy because the world is interlinked. If events of the past few weeks have taught us anything about the world economy, it is its interdependence."
You can pore over individual decisions of the Bank but that isn't the point. Long-term credibility is the point. "I do believe that interest rates have had to rise much less than they would have done had politicians still been in charge of the show because of the greater credibility of an independent system ...
"It is not a one-club policy - that is a myth. It can take account of the wider economy. The essence of the policy is to say there is no trade- off between inflation, growth and jobs."
All this perhaps, is predictable. But when you ask Mr Blair about the growing debate about whether Labour will sooner or later have to put up income taxes he is much less predictable. He is unimpressed by an argument which is audible in wide swathes of the party.
On the contrary he still regards - economy permitting - continuing reduction of taxes as a "key" objective. Luminaries like Frank Field, the former social services minister, and Lord Plant - neither exactly left-wingers - "are entitled to have this debate, but my own gut feeling is that there is a long-term trend away from higher personal tax rates."
Instead Mr Blair is excited about what private finance can do for better public services. The private finance initiative he drew up with Gordon Brown, the Chancellor, has produced the biggest-ever hospital building programme. "It is unpopular in some quarters, the unions don't like it, but that is definitely the way the world is going."
The message for the party next week will be equally uncompromising - that the Government won the biggest single party majority since 1906 because it was New Labour; and that New Labour is the "solution not the problem. We have made a very good start, we are fulfilling our manifesto pledges. We will have to hold steady over the next year or so, but we are in this for the long term".
There are plenty of potential problems ahead: the economy, and what he calls "some very tough reforms" on pensions, invalidity benefit and legal aid. "The one thing we can argue is that the country voted for New Labour ... and that is what we are going to hold to."
Acording to Mr Blair, successes for the likes of Liz Davies in the NEC ballot will be partly because they presented themselves as "critical supporters of the Government who were basically supportive. I doubt Liz Davies mentioned she was a member of Labour Briefing [the hard left group]."
Overall, he insists, he detects no desire to return to the ultra-leftism of the past. "They have certainly run on the basis they are merely grassroots supporters of the Government who want to represent ordinary party members. Let's see. If they are elected and they play a different game, they would find the party not very pleased.
"I totally understand if members decide they want some critics of the Government [on the NEC] as well as people who are part of the Government. But there is no ideological alternative I can see being put forward to New Labour."
Nor does he think there could be credible alternative _ on the neo-Croslandite old right of the party any more than on the left. Didn't Roy Hattersley and his soulmates, we asked, have a point that after years of battling to save the party, they now didn't recognise it? "They have got to understand it was never enough to make the Labour Party sane. We have to make it moden, with answers for the problems the world is posing for us," he said.
"The greatest single danger for the Labour Party of the 1980s is believing that once you excised the cancer of ultra-leftism, the task was done. In fact, all the ultra-leftism did was disguise a deeper malaise, which is the fundamental necessity for modernising social democracy. It's not simply ridding social democracy or democratic socialism from the encrustment of ultra-leftism. When Roy was in the Labour Government, they were off to the International Monetary Fund and cutting public spending. I don't criticise them for it; they were dealing with a very difficult situation.
"Each generation will find its way of renewing the basic principles. I am not saying the Croslandites are wrong, they were probably right for their time. Attlee's government was right for its time. At some later time. someone will come along and say the way the Blair government tried to do this was too old-fashioned. That's life, that's change."
That is why other countries are so interested in his "third way". Mr Blair is frustrated that the British press is more sceptical than the media in other countries; the conference he attended with President Bill Clinton on Monday was reported prominently in 40 countries round the world.
"I believe in the politics of community. That is what I am about. That is why I am not a Conservative. But you have to apply those values to the problems of the modern world."
Yet hadn't Sir Edward Heath said Mr Blair was well to the right of him? ``How do you define left?" he asks. "More tax, more spend, union power? What does he mean?" He recalled that Sir Edward was the architect of a failed attempt to reform the industrial relations laws in the 1970s. "If you define radicalism as 1960s corporatism, I don't think that is where the world is any more." His task, he said, "was about renewing social democracy." It is about recognising that social democracy has got to be a force for radical change.
As with the Croslandites so with - especially but not exclusively - middle-class critics of his long flirtation with Rupert Murdoch. Complaints of Mr Murdoch's influence on the Government were "just complete rubbish," Mr Blair said. He treats Mr Murdoch no differently to any other media proprietor. He "rejoiced" at Labour's support from business: "I was 20 years in the Labour Party when you couldn't get a businessman near it.
"The chattering classes are fine for the Labour Party but up to a point. They were really pretty reluctant about all the changes we made to the Labour Party, but were prepared to tolerate them in the interests if winning the election.
"That was never my view. That is why I have never been a partaker of the chattering classes. My view is that the changes in the Labour Party were not just necessary to win the election but were right in principle. Yes, we do have problems keeping them on board. That is why a lot of them peel off. But they are not the bedrock of the Labour Party - that is a lot of ordinary folk who are not part of the chattering classes, who pocket everything that they do ike and then moan about the 10 things they don't like."
What then of constitutional reform? Here, Mr Blair rebuts firmly one criticism - that he stumbled into Scottish Home Rule, and in doing so has now unleashed the genie of separatism. Quite the opposite says the Prime Minister. As in the very different circumstances of Northern Ireland - where to have disappointed the pent-up pre-election expectations of what a Labour government would mean might have unleashed catastrophe - so Scotland needed a way forward.
"If you offer people a choice between the status quo and separatism, there is a risk real they would choose separatism. If you offer a modern forward-looking and sensible alternative in which Scotland and England grow stronger together in a stronger UK, in my view in the end people will go for it."
The Scottish National Party, he noted, had had a bad conference. It had not set out its policies and had barely mentioned the one which truly defined it. Independence "would be a disaster for jobs, business, industry and trade." The defining moment for the nationalists had been when it had "wiped all its policies off the Internet." The other criticism is that he has "fiddled with the constitution when we should be doing other things." Not at all, he says; they all have to do with modernising and strengthening the UK.
So where does that leave us on Commons electoral reform? Here Mr Blair is notably cautious, though it is striking that he does not, this time, use the repeated mantra that he is "not persuaded" of the case for change. He will not say that the PR referendum will, or will not be in this Parliament, which will not delight those Liberal Democrats who fear it won't be. Instead the game is waiting for Lord Jenkins' report.
But he gives a strong hint that the Commons PR could be tied together with second stage Lords reform in the same referendum. Obviously, he said, the long term reform of the Lords is closely linked to reform of the Commons, because it is about the Houses of Parliament and the system of government.
Thisdoesn't seem like a Prime Minister on the point of ditching Paddy Ashdown. "I like Paddy Ashdown and I admire him. He is a good guy with good instincts for the country.
"I believe it is sensible for people who basically agree with each other to co-operate with each other. As for change to the electoral system, that has to be done only on the basis of the interests of the country."