If the pollsters have got this one wrong too, they’ll be in real trouble. For some time now, polls of London’s upcoming mayoral election have suggested that Sadiq Khan has built up a solid but hardly insurmountable lead over Zac Goldsmith.

A new poll published by YouGov today suggests that Khan's lead may in fact now be impossible for Goldsmith to reverse. The poll shows Khan with an 11-point lead in first preference votes, up from a 7-point lead in March. Once second preferences are taken into account, the poll has Khan beating Goldsmith 60-40.

More interesting than the headline figures are the results from Outer London. Both of London’s mayors, Ken Livingstone and Boris Johnson, have pursued different versions of what has come to be known as the “doughnut strategy”. Livingstone aggressively targeted inner London with policies such as the congestion charge and the Urban Task Force. In his 2008 and 2012 defeats of Livingstone, Boris Johnson pursued the inverse of that strategy, committing to expansive funding for outer boroughs, noisily denouncing Heathrow expansion and accusing Livingstone of neglecting the suburbs.

Aside from negative attacks on Khan and some rather unsavoury ethnic targeting, Goldsmith has broadly sought to adopt the Johnson template. Which makes it all the more remarkable that today’s poll has Khan leading 41-38 in outer London on first preferences, and 59-41 on second preferences.

Perhaps this shouldn't be so surprising. The most recent ComRes poll had Khan and Goldsmith level in Outer London. If Khan's support has increased across London since then, you'd expect it to have increased in outer London too, even if to a more modest extent. More fundamentally, the demographics of London's suburbs have been shifting for some time. Outer London is not as old and white as it was in 2008. The proportion of residents born abroad increased faster in outer London than inner London in the decade to 2014. The fastest increases in migrant populations have been in Barking and Dagenham, Bexley, Havering and Sutton. High rents have made young Labour-voting professionals more likely to settle down in outer boroughs.

The 2015 general election hinted at this. The four seats that Labour gained from the Conservatives – Brentford and Isleworth, Ealing Central and Acton, Enfield North and Ilford North – were all outer London seats.

So if the polls are correct the Tories should be worried – not just that Goldsmith will lose, but that their most viable path to the London mayoralty whoever their candidate is appears to be fading. Boris Johnson may have inflated the plausibility of the doughnut strategy for any Conservatives without his considerable charm: they won’t ever get to pit a candidate as charismatic as him against someone as divisive as Livingstone again.

But Labour shouldn't be jubilant yet. There’s plenty of evidence to suggest that the Conservative campaign has more favourable polling numbers than YouGov has released today. If Goldsmith thought he was a goner, it’s unlikely he’d want to spend the last few weeks of the campaign eagerly painting Khan as having extremist sympathies, and the Prime Minister might have been more reticent about getting in on the act too.

One Conservative working on the mayoral campaign told me the poll “does not reflect our polling or what we’ve been hearing on the doorstep”. On the prospect of Khan beating Goldsmith in outer London he said: “if that is true I resign from politics”.