“There’s definitely a book in that but I can’t write four books at once,” Andrew Adonis remarks mid-conversation when I enter his Westminster office. His words confirm my impression of him as a restless Stakhanovite. The Labour peer, who chairs the National Infrastructure Commission, spent the summer immersed in political activity. “Since I joined the SDP on my 18th birthday [he defected to Labour in 1995], I don’t think there’s been a time when politics has mattered more to the future of this country,” the 54-year-old tells me. After enduring divorce (on which he will not comment), Adonis has returned to the fray with renewed vigour.

The former education minister has targeted university vice-chancellors, who he accuses of operating a “fees cartel”, and Brexit, which he fears will prove an epic act of national self-harm. I discover that he is writing a book on the latter with Observer columnist Will Hutton, as well as a history of the UK’s fraught engagement with Europe since Margaret Thatcher, and long essays on higher education and political leadership (which may become extended works).

Adonis, whose lean frame led him to be nicknamed “the thin controller” as transport secretary, speaks in rapid-fire sentences that rattle along like his beloved trains. His bald pate lends him a monkish, ascetic aura. In British politics, his obsession with evidence-based policy makes him a rare creature.

After overseeing the introduction of £3,000 tuition fees in 2006, he now warns that “fees will be scrapped unless the vice-chancellors take the lead in reducing them”. He adds: “If they lead, and after all they are paid these obscene salaries because they’re supposed to be god’s gift to leadership, they will cut their own pay and cut their own fees.

“If I was leading a university now, I would be cutting fees by £1,000 a year ... I think fees could survive at a level of around £3,000, which I think is fair, right and a good deal for the young. If the vice-chancellors are pig-headed, arrogant and refuse to budge, then I think fees will be abolished. And it’s just as likely that a Conservative government will abolish fees as a Labour one.”

Adonis, who was placed in care as a child after his mother left the family (his Greek Cypriot father worked as a waiter and a postman), speaks with sincere passion of the empowering ability of education. After securing a scholarship to Kingham Hill school in Oxfordshire, he became only the second pupil since 1945 to win Oxbridge entrance.

“I was partly guilty of taking the young too much for granted,” Adonis confesses. “Though I was opposed to tuition fees of £9,000, I didn’t think that there would be a revolt against them. I now realise that the young, like other electoral groups, will only put up with so much unfairness before the sense of grievance becomes overbearing.”

For Adonis, the renewal of the generational contract must also include a chance to thwart Brexit. The former Financial Times and Observer journalist, who has become an inveterate tweeter (“Twitter is a very powerful way of forcing you to compress your thoughts”), tells me: “It’s quite wrong to think of this as a second referendum. This will be a first referendum on the exit terms. And since this is the most important issue facing the country, it’s perfectly reasonable”.

He predicts that Labour will back a second referendum, as it has embraced a meaningful Brexit transitional period. “Once Labour’s in favour it’s only a matter of time before the government has to concede…I would be very surprised if we’re not committed to a referendum on the exit terms within six months.The thing I only always learned from Tony [Blair] is ‘get the policy right and the politics will follow’. The right policy is a referendum on the exit terms, the politics will sort itself out.”

It was Blair who drew Adonis to Labour in 1995 and who, impressed by his fierce intellect, appointed him director of the No.10 Policy Unit and education minister. Though from a diametrically opposed wing of the party, Adonis speaks warmly of Jeremy Corbyn. “The young have latched onto Jeremy for a very good reason. He’s offering hope and optimism and there’s no one much else who is at the moment.”

But unlike Blair, who has conceded that Corbyn could become prime minister, Adonis maintains that the Labour leader is unelectable.“I’m not hostile to Jeremy personally, I used to be a Labour member in his constituency [Islington North], I think he’s an absolutely brilliant constituency MP. But he is not a potential prime minister. The voters have already had a chance to make a judgement on him, they’re not going to change their view in a few years’ time.”

In recent British history, Adonis notes, only former Conservative leader Ted Heath has become prime minister after first losing a general election (1966). “If Jeremy goes into another election, he will lose it. The next Conservative leader, who I cannot conceive will be as electorally unattractive as Theresa May, will beat him.

“What the Labour Party should now be doing is looking for a leader who can credibly become prime minister. We need an open contest because I can see five or six potential ones." When I ask who he has in mind, Adonis, with an eye to his Blairite credentials, tactfully replies: "I think that might be the kiss of death." And at that, as he departs to meet Labour MP and former leadership candidate Chuka Umunna, Adonis is gone.