Ken Livingstone had a piece in the Guardian yesterday stepping up hostilities in what is certain to be one of the most important domestic political events of 2012 - the London mayoral election.

The poll is of most immediate significance to citizens of the capital, since it is their mayor being chosen. But the battle, coming as it does mid-term for the coalition, is bound to become a proxy for the relative national electoral prospects of the main parties. Livingstone actively encourages that interpretation. He writes about his ambitions to run London as if he envisages heading a pioneer administration for the "new politics" that, he believes, will inevitably emerge from the combination of financial crisis and rising disaffection with the existing political establishment.

"Labour will make this election about a real alternative," the former mayor writes. It should be, in other words, a referendum on the coalition, David Cameron and the whole direction the country is taking. Livingstone is ramping up the national significance of the poll, which is a problem for Labour and Ed Miliband since hardly anyone thinks Boris Johnson, the Tory incumbent, will lose.

Opinion polls (albeit fairly unreliable at this stage since few voters have yet focused on the race) show a significant number of Labour voters preferring Johnson to Livingston. In fact, the decision by Livingstone to try to frame the contest as a kind of referendum on the general state of the economy reflects a realisation that a re-run of the personality-based prize fight of 2008 would almost certainly yield the same result. In a beauty contest (or rather a least-ugly contest) between the two quasi-celebrity candidates, Johnson would walk it.

As I wrote in the magazine last week, very senior Labour party figures are already talking privately as if Livingstone can't win. Miliband aides are rehearsing their defence, which is that the contest is indeed a peculiar celebrity face-off between two old rivals and not necessarily an accurate reflection of the national mood. Labour are confident that local elections and the vote for the London Assembly (one of the least noticed governing institutions in the country) will depict a healthy swing away from the Tories. London usually has a solid Labour vote - an island bastion of red in the south-eastern sea of blue.

But the reality is that failure to unseat Boris will be widely interpreted as a sign that the whole Miliband project is failing to gather momentum. A senior shadow cabinet member recently told me the boss's team is braced for a round of leadership speculation in the wake of Ken's defeat.

Ken might win, of course. Almost anything is possible. But it is hard to overstate how firm the consensus in Westminster is that Boris will prevail. One former member of the Livingstone team in London - and no fan of Johnson - confidently predicts his former boss will be "thrashed and humiliated". That would certainly not be a good outcome for Miliband. Downing Street is intensely focused on securing a Tory win in the capital precisely because of the effect it would have on perceptions of Labour electability. (Besides, if Johnson loses he'll be after a seat in parliament where he could cause no end of mischief for his old rivals Cameron and Osborne.)

MIliband didn't select Livingstone and the old veteran of London politics runs his own operation in the capital, so in theory the Labour leader could distance himself from a defeat. But that gets trickier if Ken's strategy is to advertise the whole thing as a dress rehearsal for the next general election, which his Guardian piece implies. Livingstone seems to think he can present himself as an outsider battling an elite establishment, bearing the flag for a different kind of politics. That is a pretty far-fetched campaign given that he has been around in London politics since the late 1960s and has already done the job of Mayor once before - not so much yesterday's man as the day before yesterday's man.

Miliband also wants to present himself as the outsider, "ripping up the rules", smashing the cosy consensus. That too is a bit far-fetched coming from someone who has never had a job - or, it would seem, much of a life - outside politics. But at least Miliband is young and unknown enough to carve out some new identity for himself. The last thing he needs is a well-known, battle-scarred veteran of old left politics road-testing his campaign lines and driving them into a ditch.