Johnson's Life of London, By Boris Johnson - You Can't Say That, By Ken Livingstone

'Playground monikers for playground politicians': Giant balloons of Ken Livingstone and Boris Johnson during the 2008 mayoral elections (PA)

The Mayor of London enjoys a "mandate over policing", according to the Metropolitan Police Authority, whose chair and vice-chair he appoints. He "remains the direct line of accountability between the Metropolitan Police Service and the people of London". Through the MPA, the Mayor's oversight covers "the appointment and discipline of senior police officers".

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In the wake of wholesale phone-hacking by agents of Rupert Murdoch's News International and resignations at the Met, the MPA referred senior officers to the Independent Police Complaints Commission. The enquiries turned on the propriety of the Met top brass's relationships, including financial, with Murdoch executives and journalists. Although the IPCC chose not to proceed in some cases, it continues with a supervised investigation into alleged police corruption, linked to the Met's Operation Weeting.

So what does the current Mayor do, at a critical moment when the force he holds to account must answer for alleged ties with the Murdoch phone-hackers? He fulfils a commercial contract for a book (duly recorded in the City Hall register of interests) with a wholly-owned subsidiary of Murdoch's News Corp, HarperCollins.

Lector, si monumentum requiris, circumspice ("Reader, if you seek his monument, look around"), advises the memorial in St Paul's Cathedral to Sir Christopher Wren – one of many notable absentees from Boris Johnson's volume of biographical sketches about history-making Londoners, from Boudica to Keith Richards. And if you seek a monument to the arrogance veiled behind the Mayor's shambolic straw-thatched bonhomie, this merry indifference to a potential conflict of interest will serve well enough.

Since we all know that the Met really bows to the Home Secretary, too few Londoners will care about any Johnson-Murdoch deal. And there's the rub: the denial of last-resort, buck-stop-here powers over core concerns of metropolitan life to the Mayor and the Greater London Assembly. Given their infantile dependence on central funds and central supervision, it's no surprise that such an air of vaudevillian frivolity still attaches to the office and the Tweedledum and Tweedledee who vie to hold it. "Boris" and "Ken", we call them: playground monikers for playground politicians. In their singular ways, both of these defective but revealing books bear witness to the puerility of London democracy.

Why should Britain's capital have, this summer, suffered the most widespread riots anywhere in the developed world since the global downturn began? Read the gruellingly exhaustive memoir by the two-term former Mayor or the lightweight batch of essays about his London heroes (in effect, a kind of autobiography) by the incumbent, and the implicit answer would seem to be: Search me, guv. Livingstone will drone on about the distortion of his crime-reduction policies by the reactionary press, the post-industrial extinction of "skilled working-class jobs" and the hounding of his favourite adviser, Lee Jasper. Johnson will harrumph about the unruly lower orders' propensity to mayhem and the city's "sub-tectonic paganism and wildness" since the Roman legionaries quit in the fifth century.

Neither has the guts to say: something went badly wrong on my watch, and we should fix it now (although Livingstone refers to events as recent as the Norway massacres in July). Orotund pseudo-erudite Etonian wiseacre, or chippy, cheeky Sarf Lunnon urchin: you pays yer money and you takes yer choice. Next May, we will. Still, the capital deserves a better one.

Both books offer eccentric stand-up turns in place of statesmanship. But if the Whitehall and Westminster fiscal stranglehold limits London's mayor to a bread-and-circuses role of entertainment on the fringe, many voters might prefer an act with laughs. Trivial and derivative it may be, but Johnson's sketchbook diverts as well as annoys. Livingstone's doorstop apologia will try the patience of the most obsessional geek. On this showing – dementedly pedantic score-settling in the Red corner, mildly amusing patter in the Blue – Johnson would walk it in the spring. But neither narcissist should get another chance.

Surprisingly often, the gulf between them looks, on closer inspection, more like a hairline crack: Freud's narcissism of small differences, writ large. Johnson's sheaf of leading Londoners includes three women. First comes the insurrectionary queen of the Iceni. It turns out that Boudica's anti-Roman revolt was an early example of "banker-bashing aggression" in indebted Londinium (Johnson's fondness for the cheesy anachronism lowers the history in this romp to sub-Python level). Then, in Victorian times, we meet Florence Nightingale and Mary Seacole. The iconic nurses – one white, one black – share a chapter.

As a thumbnail summary of the past 30 years in Britain, you might say that the right won the economic arguments while the left won the cultural ones. Here's the perfect instance. Johnson doffs his cap to the history of diversity, to which Livingstone first gave an official stamp during the GLC era that ended in 1986. Without Livingstonism and its legacy in London, the Jamaican Mary Seacole – beloved "Mother of the Army" in Crimea – would never have starred in his enemy's book. Neither would the Mayor refer routinely to the "homophobic venom" that (so he thinks) led early-Christian Londoners to dump a bust of the Emperor Hadrian in the Thames.

When it comes to wealth and its creators, Johnson does love the bankers to pieces – but then so did Livingstone in his City-lunching phase before the slump. Two chapters laud the virtues of financiers: on Richard Whittington, four-times Lord Mayor and medieval tycoon turned philanthropist, who made 60 loans to the government; and Lionel Rothschild, who funded the purchase of the Suez Canal company. Inevitably, you will fail to find trade-union leaders such as Ben Tillett or Tom Mann in a book that refers to the Docks "seething" with union activity like some toxic cauldron. Nor will you encounter London's great literary visionaries: Milton, Blake, Dickens – still less that adoptive Londoner, Karl Marx.

John Wilkes, the Georgian hell-raiser and "father of civil liberty", does rate a full chapter as the radical counterpart to "compassionate conservative" Dr Johnson. Even so, this Johnson is keen to show how the anti-authority firebrand cooled down as a Lord Mayor who suppressed the mob. We glimpse the elder Wilkes, now "a pillar of the Establishment", but still engaged on "feline prowlings between the houses of his various mistresses and offspring". No London journalist-cum-politician could ever behave so scandalously today, of course.

Yet, despite the Mayor's gung-ho celebration of plutocratic accumulators from the Claudian invasion to the Big Bang, Johnson and Livingstone can still sound like twins under the skin. As his key idea, Johnson propounds a theory of London as an urban machine of creative emulation: a "cyclotron" for incoming talent. In the city's febrile financial, political and cultural markets, from Shakespeare's theatres to the recording studios of Keith Richards (who is praised for his tax avoidance), the hunt for glory and distinction drives innovation. So London incubates and rewards a "constant competitive urge", a "frantic desire for praise, recognition and money", while "the eternal gap between rich and poor" – which the Mayor accepts as complacently as any Victorian hymn-writer – forever yawns.

Now turn to Livingstone's elephantine memoir, in which a diary of our young hero's hitch-hiking trip through Africa in 1966 occupies 30 brain-numbing pages. From first to last, "Ken" bears out the "Boris" line on London. Livingstone displays not a modest socialist's delight in fellowship but a fiercely antagonistic will to win. He exposes so much rivalrous, ambitious esprit de l'escalier in answering critics that his staircase of belated put-downs would reach higher than Renzo Piano's 1000-foot glass Shard – "one of the most beautiful modern buildings in the world". He championed that monstrous protuberance when as Mayor he turned cheerleader for speculative skyscrapers, and the billionaire developer's best friend – another strike in favour of the Johnson thesis about London's elite competitors.

In the words of Anthony Trollope: he knew he was right. Via a punishing trawl of the archives of the Mail, Standard, Sun and every other lickspittle organ of the ruling class, Livingstone shouts back against each abusive headline and character-assassination comment piece. Yes, the right-wing papers lied shamelessly about him. Their libels began in the gutter and descended to the sewer (though not Joseph Bazalgette's noble network, to which Johnson devotes too little space). They traduced and twisted sensible urban-renewal, cultural-inclusion and mass-transit policies that would have failed to raise the eyebrow of any Democrat city boss in America. So what did "the most odious man in Britain" (The Sun, 1981) end up inflicting on his hapless fiefdom? The Oyster Card!

Were the rebuttals a tenth their length, and the disputant above suspicion, Livingstone's prolix self-justification might convince. He flays any opponent who voices a racist or otherwise bigoted sentiment. But in 2006, he fell out for once with property magnates: the Reuben Brothers. What did he say about the pair, born in India and of Iraqi Jewish origin? "If they're not happy here, they can go back to Iran and try their luck with the ayatollahs, if they don't like the planning regime or my approach." In his book, where every faint hint of prejudice comes under screeching scrutiny, he euphemistically admits that "To get the issue into the media I made a crude personal attack on them, which... put the Reubens in the spotlight they hated". So that's alright then, Ken?

The surly nit-picking of his vindication leaves no room for a vision that might stir the sceptics. Except once, when Livingstone simply quotes his post-atrocity speech in Singapore (just after the Olympics triumph) addressing the 7/7 bombers: "Nothing you do, however many of us you kill, will stop that flight to our cities where freedom is strong and people can live in harmony with one another". This was his finest hour. If only a few more passages in this sectarian and solipsistic work had come within an octave of that note.