Ukip leader Nigel Farage has said his party would prop up a minority Conservative government if it agreed to a "full, free and fair referendum" on Britain's EU membership.
It follows a Survation poll for the Mail on Sunday which found that one in four Britons back Ukip.
The eurosceptic party won a by-election in Clacton with a giant 12,404-vote lead.
Private polling analysis seen by The Sunday Times puts the party on course to win 25 parliamentary seats at the next election.
While far less than predicted in a study for the Mail on Sunday, this is still far higher than previous predictions.
Douglas Carswell, who defected from the Conservative party and won back his seat as a Ukip candidate, has been introduced to the Commons.
As Ukip prepares to enter Parliament for the first time, leader Nigel Farage reflects on his party's byelection successes.
Ukip has its first elected MP after Douglas Carswell took almost 60% of the vote in the Clacton by-election.