The YouGov poll in the Evening Standard today shows Johnson is up two points on last week's rating to 49 points, with the Mayor down one point to 36.
The Mayor's campaign said it was launching an official complaint against YouGov to the Market Research Society, accusing the poll firm of using "flawed methodology" and that its polls were "totally out of line with polls using established methods".
The Livingstone campaign team cited an ICM poll from last week that showed the Mayor and Johnson to be neck and neck. As examples of the flawed methodology it said that YouGov over estimated the number of Londoners to be aged 55 plus, putting the figure at 39% compared to the Office of National Statistics, which estimates the figure is 26%
The Mayor's team also said YouGov do not take account of the much larger ethnic minority population in London.
A spokesperson for Ken Livingstone said: "This is because YouGov's methodology is fundamentally flawed. These and other mistakes mean that they consistently over estimate support for the Conservatives in London compared to established polling techniques and, as last week, we clearly reject this poll.
"YouGov's polls are misleading the public and we have therefore decided to make a formal complaint about their basic flaws."
If the latest YouGov poll were to be proved correct it would put the Tory candidate Johnson on course to be the next Mayor of London.
However, according to the Standard even the Tories' own polls "put the two main candidates much closer" than YouGov.
In response to the Livingstone complaint YouGov president Peter Kellner said that the Mayor's team were using the row to divert attention from their struggling campaign.
"This is a diversionary tactic to get people talking about the row rather than their campaign, which is in deep trouble.
"I will wait and see if they complain to the MRS and if the MRS thinks it is worth pursuing then we will respond to the MRS."
He said YouGov was first made aware of objections by the Mayor's team last week and the market research adjusted its profiling on the two areas cited, namely age and ethnic minorities.
"I take the view that we are not infallible and we looked in detail at our age and ethnic profiles, which we changed accordingly. Those changes are reflected in today's poll which show Boris Johnson's campaign 13 points ahead."