"It looks certain to me that Sadiq will win," one Labour MP said recently. Her Conservative counterparts agree. It is increasingly common to hear Zac Goldsmith bemoaned as "low energy", the term used to dismiss Jeb Bush's candidacy by Donald Trump, the presumptive nominee.

The difficulty for winning London as a Conservative, as one veteran observes, is that "our path to victory runs through people who don't necessarily think of themselves as Londoners - they leave the city at the weekend rather than heading to the city centre, and if it looks a shoo-in for Labour, they'll stay home". "Zac," they observe mournfully, "is running a very good campaign to get a pat on the head at the end from the Economist and the Standard of the kind that Steve [Norris, the defeated Conservative candidate in 2000 and 2004]. But not to win."

Certainly, if the polls are to be believed - particularly YouGov, which many key personnel on both sides believe is the only pollster capable of accurately polling London's highly mobile electorate, which moves often and is harder to pick up through telephone polling than elsewhere - Khan is heading for a crushing victory over a candidate who seems to be running a largely colourless campaign.

But there is a growing fear among Labour politicians that the polls could again be wrong. That's in part because, as John Bolton once observed, "politicians, like generals, tend to fight the last war". The notion that the polls were wrong, before the election, was dismissed as a conspiracy theory by many of Ed Miliband's closest aides. Now, that worry feels mainstream.But it goes deeper - many MPs from minority backgrounds in particular are nervous.

There is no bedrock of data to draw on - we can't know if ethnic minority candidates in London constituencies have underperformed their poll ratings, as for the most part, there is little constituency polling to judge against the real results. No serious ethnic minority candidate has stood for the London mayoralty before. Ram Gidool, of the Christian People's Party, finished fifth in London's inaugural elections in 2000, while Winston McKenzie, a political vagabond who first joined Labour, then the Liberal Democrats, then the Conservatives, before running for the London mayoralty as the candidate of Robert Kilroy-Silk's Veritas, came last in 2008.

But still, Labour MPs worry that, in the words of one "That people will say 'I'm voting Labour, and then they'll see the name 'Khan' and vote for someone else." They worry about a British version of the "Bradley Effect" - where voters tell pollsters they are happy to vote for ethnic minority candidates, before opting for a white candidate in the polling booth.

Are they right? Who knows. But as far as the polling of London is concerned, one thing is being overlooked. "YouGov and the rest are trying to fix what went wrong," says one senior staffer at Labour headquarters, "But they haven't fixed it yet, not for certain. That means that the overestimation of Labour's vote share could still be happening. The error is still there."

Despite his "low energy" campaign, Goldsmith's chances may be better than they look.