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"You’re making me feel under-dressed,” teases Tony Blair at the sight of a visitor wearing a tie. The former prime minister is, inevitably, tieless but dressed to kill in jeans, tailored jacket and brown Chelsea boots. With his slim figure and tan, he could pass for an ageing rock star or dot.com billionaire.

We meet in his central London offices which have the feel of a boutique hotel. The cream carpets are plush, there are photos with Mandela and faith leaders, and paintings by Andrew Gifford of the skylines of Jerusalem and Ramallah. He tells us his foundation has more than 200 people working all over the world and he travels regularly. Today, however, his attention is focused on domestic politics and especially Brexit.

“I was Prime Minister for 10 years and I can’t think of a single law that I wanted to pass that Europe told me I couldn’t, or any law they made me pass that I didn’t want to,” he said, exasperated that Brexiteers have created a “myth” that Brussels meddles constantly in the British way of life. Europe had zero say on the NHS, education and taxes.

He was also frustrated by Jeremy Corbyn’s latest European policy concoction, the idea of a future referendum on a yet-to-be-negotiated deal with no clue as to whether a Labour premier would support or oppose his own agreement.

“Imagine the Labour candidate on the doorstep,” he cried, parodying the sales pitch: “‘We don’t want a referendum, we want an election to have a referendum and then before the referendum we’re going to negotiate this new deal with Europe — the Jobs First Brexit — because we’ll be better negotiators than Theresa May and Boris Johnson.

“‘So, we’re going to negotiate this new deal, then we’re going to put it in a referendum but when we come to that referendum, we can’t actually tell you whether we’re for the deal we’ve just negotiated or not.’” He concluded with understatement: “Now, I would find that difficult on the doorstep to argue.”

For this reason, he thinks next week’s Labour conference in Brighton will be “probably the most important conference in living memory”.

Moreover, the dangers to Labour if its leader blunders into “a Brexit election” have increased following Jo Swinson’s first conference as Liberal Democrat leader this week. Her promise of a “very, very clear revoke” could be “attractive” and he thought a “resurgent” centre party could squeeze Labour.

Boris Johnson, however, had been “boxed in” by the cross-party alliance in Parliament and was having to negotiate a withdrawal deal. “I think he is trying now to do that,” said Mr Blair.

“I don’t think he was before.”

For now, the threat of a no-deal Brexit was off the table — but only as long as Mr Corbyn does not hand the PM an election. “It isn’t off the table if you have a Brexit general election,” he said urgently. “It’s back on the table. Now he [Mr Corbyn] may say, ‘but I’ll win the election’ … but the one thing for sure is that this election is probably as unpredictable as any you could ever imagine.” The answer, Mr Blair argues, is to kill off no deal for good with a new referendum.

He sounded almost nostalgic for the Tory Party of David Cameron, whose book he had been reading. “The extracts I’ve read have been good, he’s obviously written it himself, he’s thought about the issues deeply.”

There is a sense of kinship in his tone. “I know myself it’s difficult. You’re in government, you make decisions, people criticise you for it. Although I didn’t agree with the decision to hold the referendum, I think he genuinely felt that it had to be done for the country.”

He did not hold Mr Cameron responsible for the defeat of Remain. “I say, no, the people responsible for it are people like Boris Johnson — who didn’t particularly believe in it but were prepared to put the whole future of the country at risk by advocating Brexit, when any sensible, serious politician who has been in and around government, knows that the idea of Britain ripping itself out of the largest commercial and biggest political market right on its doorstep, is a terrible regressive backwards step for Britain.”

He thought Mr Johnson could get a deal but it would be either “a version” of the thrice-­rejected withdrawal agreement or it would mean separating Northern Ireland from the rest of the UK, giving nationalists “an extra dimension” to erode the Union.

He hoped soft-Brexit MPs like Stephen Kinnock, who founded Labour MPs for a Deal, would come round to backing a referendum instead. “In sort-of spiritual terms, if you like, I completely get where they’re coming from. They want to find a reasonable way through a horrible problem.”

His own preference is a confirmatory ballot, and he thought the best chance for it was to force Johnson’s hand when he wanted to ratify a deal.

Another route to demand a referendum could be via a “government of national unity”, though he thought it was “unlikely” unless Mr Johnson wilfully breaks the Benn law designed to outlaw no deal. Asked who could lead such a government, he said Mr Corbyn could not “command support across the Commons”. Naming candidates was “invidious” but he mused that an elder Labour statesperson with no long-term ambitions had the best chance.

A referendum was winnable, he believed, but what about Labour — would it win the general election? He fell quiet. “I don’t know. Look at my disagreements with Labour’s policies, positions, my dismay around anti-Semitism — I mean all that alone. I think Labour’s got a challenge whenever the election is.”

Did he want Labour to win? “Look, I always want a Labour government, but it’s got to be a Labour government that’s doing the right things for the country.”

Mr Blair said he had “always” voted Labour. “It’s hard for me to imagine ever not voting Labour but I don’t hide the disagreements, the profound disagreements I’ve got with aspects of how the Labour party has been led in these past few years.”

Sounding less comfortable, he added: “If you have a Brexit general election … Brexit for me is the most important thing but I’ve always voted Labour.” He seems conflicted. When did he last talk with Corbyn? “I don’t know really, a long time ago, I should think. I’ve nothing against speaking to him.” Was he surprised by the more centrist positions taken by shadow chancellor John McDonnell on issues including a referendum? “Rightly, he’s making strategic calculations.”

He was appalled by the spread of trigger ballots to oust centrist MPs and the NEC decision to dump ­Student Labour, a bastion of Blairites.

“The last thing you should be doing is putting decent MPs at risk, causing trouble. It’s madness, so no I don’t agree with what they’ve done on Labour Students — it’s very foolish.”

We suggested he and Mr Cameron were both leaders whose domestic achievements were overshadowed by single-issue controversies, in his case the Iraq War. Mr Blair seized on the questions: “Look at the things that we did: minimum wage, gay rights, the biggest ever constitutional programme, largest ever investment in health and education. We reduced child poverty, we reduced pension poverty, the Good Friday Agreement, we did a whole host of things.”

His staff are keen to move him on to his next appointment. Mr Blair leaves with news that he’s recently become a grandfather. “It’s amazing,” he beamed. “It’s the one thing in life that lives up to the hype.”

Asked if he changes nappies, he smiled and displayed the same old deft ability to slip away from a tricky question. “I’m very hands-on but the great thing about grandchildren is that you can give them back.”