The telephone poll by polling group ComRes found 43% of respondents planned to vote for UKIP next month, with the Conservative Party looking a distant second on 30%.
It was widely expected that Rochester & Strood would provide a more difficult challenge for UKIP leader Nigel Farage. Even after UKIP romped home in Clacton to gain its first-ever member of parliament, earlier polls in Rochester put UKIP ahead of the Conservatives by just 9 percentage points. The UKIP lead has now increased to 13 points.
News of a slip in the polls will be particularly embarrassing for the Conservatives as they struggle to hang onto a seat they comfortably won with a majority of 10,000 votes at the last election. Mark Reckless, the man who won it for them in 2010, is now standing as UKIP's candidate after a high-profile defection in September.
Underlining the stakes, Prime Minister David Cameron made his first trip of a planned five visits to the constituency last week in a concerted effort by the Tory leadership to woo voters back ahead of the by-election. Cameron has promised to "throw everything we can" at the campaign.
In a speech to activists last month he said:
I would say one other thing to those people - you have got elected with the help of Conservatives, who stuffed envelopes, who walked streets, who knocked on doors, who worked their guts out to get you to be a member of parliament, you have let those people down. We are coming for you in by-elections and we are going to throw everything we can at you.
So far this strategy appears to have harmed his chances. Here's another ComRes poll question:
