The leaked poll was shown to a select group of Tory activists campaigning for Bailey to be the next London Mayor.
It surveyed 2,000 voters in the city, who ranked the candidates on first preference.
The first round of voting showed Khan with 42 percent support among voters, with Mr Bailey at a close 35 percent.
On the second round of voting, where the lowest supported candidate is eliminated, Mr Khan’s support jumped to 55 percent, whereas Mr Bailey’s surged to 45

The Tory backing Sunday Telegraph revealed the data was shown to the group of activist last weekend as Mr Bailey prepares to ramp up his campaign.
The newest data shows a boost in the polls for the Tory candidate, with a YouGov poll conducted in March giving Mr Bailey 23 percent of support among London voters.
An August poll from Redfield and Wilton that surveyed 2,500 voters gave Khan 49 percent support, compared to Bailey’s 26.
Speaking to the Sunday Telegraph a source said:
“While we don’t comment on internal polls, I would say that no one in the campaign is complacent.
We have a long way to go in this race, and that means Shaun and the Bailey campaign team getting the message out week in, week out.
With record crime rates and Khan’s appalling handling of TfL, we owe it to Londoners to be the change they desperately need.”
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