UKIP leader Nigel Farage said he would demand that Cameron bring forward a planned referendum on EU membership from 2017 to next year if UKIP polled strongly and the prime minister needed its support to stay in office.
"I'm not prepared to wait for three years. I want us to have a referendum on this great question next year and if UKIP can maintain its momentum and get enough seats in Westminster we might just be able to achieve that," Farage told the BBC.
Read MoreUKIP: From 'clowns' to contenders
UKIP's rise threatens Cameron's re-election drive by splitting the right-wing vote, increases the likelihood of another coalition government, and poses a challenge to the left-leaning opposition Labour party in northern England too.
It also adds to pressure on Cameron from within parts of his own party to become more Eurosceptic.
Cameron has promised to try to renegotiate Britain's EU relations if re-elected next year, before offering Britons a membership referendum in 2017. But some of his own lawmakers want him to take a tougher line and to bring forward the vote.
UKIP won European elections in Britain in May, has poached two of Cameron's lawmakers since late August, and will try to win a second seat in parliament in a by-election next month.
Before Sunday, most polling experts had forecast it could win only a handful of the 650 seats in parliament in 2015.
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But based on the result of a Survation poll for The Mail on Sunday, the party could win more than 100 seats in 2015.
The poll put UKIP's support at 25 percent, 2 percent higher than a similar poll in September.
Support for the Conservatives and Labour was tied at 31 percent, according to the poll, which was based on interviews with 1,003 people nationwide.