Labour has posted a 12-point opinion poll lead over the Tories - its widest margin of advantage in a ComRes survey for more than seven years.
The Opposition gained two points to 43% on a month ago and the Conservatives dropped two to 31%, in the poll conducted for the Independent on Sunday and Sunday Mirror.
It showed the Liberal Democrats static on 10% and Ukip down one on 8%.
Two thirds of voters also backed a cut in British contributions to the EU as Prime Minister David Cameron prepares for a Brussels summit next week to discuss the future budget.
Tory rebels joined forces with Labour last month to defeat the Government by pushing through a call for a real-terms cut. Mr Cameron is arguing for a real-terms freeze.
In the poll, 66% said UK payments "should be cut rather than frozen" with 12% against and 22% unsure.
A majority (58%) also agreed that Britain should withdraw from the EU altogether "if some EU powers cannot be restored to the UK", including a 53% majority of Labour voters.
Even Liberal Democrat voters backed that stance by a margin of 39% to 32%.
Asked if the UK should "leave the EU regardless", 43% agreed - with more Tory and Labour supporters backing the policy than not.
While nearly a quarter (23%) of Lib Dem voters agreed, a clear 57% were opposed.