At 8am on 7 May 2016, Sadiq Khan walked into the Mayor of London’s office for the first time since being elected. A framed portrait of a “Boris bus” was taken down. The remnants of Ken Living­stone’s wine collection were removed. But it was what was absent that struck his team. “There’s no handbook on the shelf called How to Be Mayor,” an aide recalled. “It’s learning by doing.”

Khan’s victory had immediate potency: he was the first Muslim to lead a Western capital city. Yet he was determined to be “more than a symbol”. Since entering City Hall, Khan has frozen Transport for London fares until 2020, launched the Night Tube, announced the new £10 “toxicity charge” on the most polluting vehicles and invested heavily in skills for the city’s workers.

No cause animates him more than solving London’s housing crisis. In 1968, Khan’s Pakistani immigrant parents secured a council house in Tooting, the constituency their son was later elected to represent in parliament. After saving for a deposit, the Khans bought their own property for £13,000. Too few, the mayor often laments, have that opportunity today. In London, where the average house costs over £600,000, home ownership has fallen from 60 per cent of the population in 2000 to roughly 45 per cent.

On the morning of 3 May, just before the first anniversary of his election, I joined Khan at County House, Beckenham, in the southern suburbs of London. The mayor was at this block of flats to meet the first tenants to benefit from his London Living Rent. “I thought it was too good to be true,” Emma Mahama, a 29-year-old NHS worker, said of the scheme, which pegs rents at a third of the average local wages. Under a deal negotiated between Khan and the owners of County House, rents are set at £965 a month for a one-bedroom property and £1,072 for a two-bed, compared to average rents of £1,300 and £1,550 elsewhere in Beckenham.

As Khan met tenants in the spacious flats, he emphasised that the policy – inspired by a similar one introduced by the mayor of New York, Bill de Blasio – was designed to allow them to save for a deposit.

Speaking to the mayor, who was dressed in his trademark outfit of open-necked white shirt and dark suit, I asked whether the job had fulfilled his expectations. “It’s been amazing. I don’t want to pretend that it hasn’t,” he said. Khan, who is 46 and a boxing aficionado, spoke excitedly of the 29 April heavyweight fight between Anthony Joshua and Wladimir Klitschko at Wembley (he congratulated Joshua personally in the ring). “History was made because of the biggest-ever boxing match in [postwar] history – 90,000 people. We made that possible because of getting the trams, the trains, the Tubes, the coaches, the council to work together . . . The world is now seeing a global city hosting massive events.”

Khan, who was little known in Britain before standing for mayor, swiftly became a figure of global prominence. In the US, which he visited last September, the Beltway is fascinated by the rise of a Muslim politician in the age of Donald Trump. Among the journalists in Beckenham was the New Yorker’s Sam Knight, who is profiling Khan for that magazine.

The mayor spoke with pride of having appointed the first female Metropolitan Police commissioner in the force’s 188-year history (Cressida Dick) and also the first female fire commissioner (Dany Cotton). Khan, who has two daughters – aged 17 and 15 – is a passionate feminist, a cause he dates back to his childhood, when he and his six brothers shared the housework and cooking with their sister and mother. “We never thought we were superior because we were boys.”

The biggest surprise of the job, Khan said, was “how bare the cupboard was”. Only 4,880 of the homes completed and 13 per cent of those given planning permission in Boris Johnson’s last year as mayor were “affordable” (Khan has increased this to 38 per cent and adopted a more stringent definition of “affordability”). “Whatever you say about Ken Livingstone, his foresight meant that Boris Johnson could cut some ribbons when he was the mayor – these things take years. I’m cutting no ribbons, because Boris started nothing during his eight years.”

His management style grates with some. The mayor takes decisions with a close-knit group of senior aides and his relationship with the London Labour Group has been acrimonious at times. A London Assembly member told me the mayor still does not “really understand how City Hall works”.

Although he is proud of his record of never having lost an election he has contested – since he first stood for his school council, aged 11 – 2016 was a year of defeats. Against his choice, the UK voted to leave the European Union and Jeremy Corbyn was elected as Labour leader for a second time (but Khan maintains that he does not regret nominating the left-winger in 2015 – a decision that led some MPs to accuse him of opportunism). Then, in November, Donald Trump was elected as US president. I asked if Trump had proved as bad as he feared.

“His first 100 days haven’t gone according to his plan,” Khan said diplomatically. “It’s in nobody’s interests for America to struggle. It’s in nobody’s interests for America not to be a positive influence in the rest of the world, and I’m hoping President Trump takes wise counsel and changes course.”

He added: "I’m disappointed that our Prime Minister, Theresa May, invited him on a state visit so quickly. Compare and contrast with previous state visits from the president of the US and when they took place.

"I recognise the special relationship we have with the USA. That special relationship means being able to say boo to a goose, calling out people when they’re wrong, not just simply being a sycophant. Of course you stand shoulder to shoulder with them at times of adversity but I think Prime Minister May should have called him out [over the Muslim ban]."

“Will London fall?” was the headline on a recent New York Times report about the effects of Brexit. Did Khan believe the capital’s status as a first-rank global city was threatened? “Yeah, it is, especially if it’s an extreme hard Brexit,” he said. “One of the things that we did on 24 June, the day after [the referendum], was begin a campaign – three simple words: ‘London is open’. The idea is to show the world that even though we voted to leave the EU, we’re not going to stop being open-minded, outward-looking; we’re not going to stop being a place where you can come to invest. We’ve got the best talent.” He continued, “It beggars belief. We’ve got a million Londoners who are EU citizens, who, a year on, haven’t been given a guarantee about their future. [May] should be giving them a cast-iron guarantee. Don’t be surprised if they leave here and go back to their countries of origin.”

Khan, who recently visited Brussels to meet the European Commission president, Jean-Claude Juncker, and the Brexit negotiator Guy Verhofstadt, and met Emmanuel Macron in Paris, warned: “We are leaving the EU [and] there will be consequences. It’s not conceivable that the UK could have a better deal outside the EU than we had before. We’ve got to recognise that. I’m afraid the aggressive pandering that the Prime Minister and her team have adopted doesn’t bode well for a successful, fruitful negotiation.”

The mayor praised the shadow Brexit secretary, Keir Starmer, whom he has known since their days as lawyers, for recognising “the importance of privileged access to a single market”. But he added: “There is an issue on the doorstep . . . Everyone is clear about my position in London, you know where you stand with the Tories – extreme hard Brexit – [and] you know where you stand with the Lib Dems: they wish the referendum had never happened and want a second one. People are less clear about ­Labour’s position nationally.”

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I asked Khan whether, like Tony Blair, he regarded a Conservative general election victory as inevitable. “The polls show a massive lead for the Conservative Party. That’s the reason Theresa May called an election,” he said, expressing no hope of Labour defying expectations.

Among those standing for the Tories is Khan’s erstwhile mayoral opponent Zac Goldsmith. “Just look at his record over the last year and a half,” Khan said of the man who framed him as a friend of Islamist extremists. “Here is the man who was the candidate for the nastiest, most divisive campaign – according to commentators and political experts – that the country has seen for at least a generation. He’s somebody who believes in an extreme hard Brexit and the voters in Richmond Park don’t want a candidate with extreme hard Brexit views.”

Unlike some in his party, such as Jon Cruddas and Clive Lewis, Khan rejected a “progressive alliance” involving Labour standing aside for other left-leaning candidates in selected seats. “There should be no no-go areas for Labour . . . We had a campaign in London, just last May, when we were encouraged not to go to Tory areas. It was possible for me to win the mayoralty by just focusing on the so-called Labour boroughs but I refused to do so . . . I’m in Bromley today, Tory Bromley, unveiling the first London Living Rent homes. That’s the difference good leadership can make.”

Among many in Labour, Khan – the party’s most senior elected politician – is increasingly spoken of as a future national leader. Allies say both that he wants the job and that he has the credibility required to make the opposition electable once more: polls show him to be the party’s most popular politician. But he knows that the mantle of “leader-in-waiting” is one best avoided. “I’ve got the best job in the world. Why give up the best job in the world to be Labour leader?” he said. And asked whether he would stand for a second term in 2020, he didn’t miss a beat: “Absolutely.”

George Eaton is writing a biography of Sadiq Khan