Ken Livingstone, the figure who was until recently probably the most successful leftwing politician in Britain since Aneurin Bevan, enjoys his retirement by appearing on talk radio, getting himself suspended from the Labour party due to offensive historical speculation, and writing oddly charming books. In Livingstone’s London, the former mayor and leader of the Greater London Council, who has (through the GLC and Greater London Authority) spent more time in charge of the capital than anyone else, gives a cosy and mildly eccentric account of the city he has shaped more than any other living politician.

Of Livingstone’s many books, this one shows the least influence of ghostwriters, and his resignation from Labour means he clearly feels no pressure to maintain a political line. So whereas the compendious You Can’t Say That veers suddenly from an honest and often hilarious memoir to a slick manifesto for his failed re-election bid of 2012, this is just Livingstone rambling about a variety of London-related subjects – history, industry, “regeneration”, food, buildings, transport, views, theatre, blue plaques, music, racism, capitalism and, obviously, newts – in a roughly chronological narrative. He goes from baby boomer schooldays through to some optimistic words about Jeremy Corbyn and his old GLC comrade John McDonnell, which suggests he’s not bitter about his suspension. The idea is obviously a series of fireside chats, in the style of one of his heroes, FDR – though when he ponders which historical figures he’d like to have dinner with, he opts for the more interesting pair of JFK and Lenin.

This is enjoyable in places, but disappointingly the book has very little detail about the contribution he himself made to today’s London – or even really whether he approves of what happened to it under his watch. Things just seem to occur – such as the Shard, a grotesque developer’s fantasy project that Livingstone enthusiastically backed in order to get a redesigned London Bridge station out of the proceeds, symbolising his Faustian second incarnation, where we got oligarchical skyscrapers in return for better bus stops. How we got here from his radical tenure at the GLC of the 1980s – which Margaret Thatcher regarded, as he amusedly quotes more than once in this book as an “eastern European” style “tyranny”, for crimes such as lowering bus fares and supporting the ANC – is never really explored.

In a chapter on the City, Livingstone laments that Tony Blair and Bill Clinton “believed that they had to work with the giants of Wall Street and the City of London” – but the City expanded its powers hugely during his mayoral terms. Livingstone had little control over this, but he did have control over the many deals he struck with property developers, where what his successor would call “Dubai-on-Thames” was erected and then given a tiny fig leaf of “affordable housing”, a policy that is still in place.

Boris Johnson ran London as the Macmillan to Livingstone’s Attlee, placing a more rightwing emphasis on what were mostly unchanged policies. There is obviously no love lost between these two, and in the passages where Livingstone outlines the relentless campaigns Johnson and the Evening Standard ran against his administration, he is clearly still furious that he was swindled out of the mayoralty by a well-connected chancer. However, the London mayoralty is still what Livingstone made, and Johnson and Sadiq Khan continued – official multiculturalism, better tubes and cheaper buses, growth growth growth, and social goals supposedly wheedled out of developers through percentage deals. The poverty and social tensions with which Livingstone ends his little London guide suggest this is no longer good enough; far more radical ideas are coming today out of northern cities like Preston and Salford.

There is minor score-settling here too, which involves defensiveness about the charges of antisemitism that got him thrown out of the party, but no explanation. There are also several accounts of allegedly poor quality behaviour from Margaret Hodge. But there is no self-criticism when it comes to the London he made. Instead, we get some funny anecdotes – especially in a chapter on his favourite restaurants – interspersed with a familiar series of tales about social democratic London heroes such as Herbert Morrison and Frank Pick. There’s a similarly familiar if heartwarming narrative about a brutally unequal city reforming itself in the postwar decades through council housing and municipal provision, and a racist, imperial city becoming in a few decades one of the most successful multicultural capitals in the world. But if you have a father or uncle who was born in London and involved in left-wing politics, he could write you much the same book.

I remember well the 2000 mayoral election, where Livingstone won a landslide as an independent. It was the first time I ever voted, at the age of 18, and I still have my “Livingstone4London” campaign badge. His battle against the ballot-rigging that Blair imposed to keep him off the Labour ticket was inspiring, and so too was the legal battle he fought against Gordon Brown’s moronically ideological plan to part-privatise the tube (ironically, it would be re-nationalised under Johnson when, as Livingstone predicted, the quasi-private company Tube Lines collapsed). Inspiring too, in a less dramatic way, was the huge improvement in the buses. But the real point for the left was that he was one of us. London became a global capital of inequality under his watch, but we assumed he did what he could. When he writes in this book that “I never learned to drive, so all my life I’ve used public transport. I don’t see any point in being caught in traffic jams when the alternative is to sit on the bus or tube and read a good book,” I still think: “That’s who I want running London.” Much more than Blair, he made global capitalism nicer – neoliberalism with a socialist face. A left that wants to go beyond facades and Faustian pacts urgently needs a serious account of what Livingstone did and didn’t manage to get away with. Sadly, they won’t find it here.

• Livingstone’s London by Ken Livingstone is published by Muswell (RRP £8.99). To order a copy go to guardianbookshop.com. Free UK p&p on all online orders over £15.