LONDON (REUTERS) - New policies floated on Sunday suggest Britain's Prime Minister David Cameron could respond to a mid-term election defeat by seeking to win back right-wing voters, despite a pledge not to lurch to the right.

Mr Cameron's Conservatives were beaten into a humiliating third place on Thursday in a vote for the vacant parliamentary seat of Eastleigh by the right-wing, anti-European Union UK Independence Party (UKIP). The seat was won by Cameron's pro-EU, centre-left junior coalition partners, the Liberal Democrats.

Conservatives fear that if Mr Cameron does not shore up his right-wing base, UKIP could split their vote and stop them from winning a majority at the next general election in 2015.

The result piled pressure on Mr Cameron from party members who want him to ditch policies such as legalising gay marriage and promoting clean energy, and focus on traditional Conservative themes such as tax cuts and fighting Britain's corner in Europe.

"The battle for Britain's future will not be won in lurching to the right," Mr Cameron wrote in an article published in the Sunday Telegraph newspaper. "So tacking right or left is not an option. And neither is abandoning the course we're on."

Mr Cameron said his government would stick with key policies such as cutting the welfare bill to reduce the deficit, curbing immigration and reforming education.

But front-page articles in three Sunday newspapers suggested that despite Mr Cameron's words, his party was responding to the Eastleigh by-election by putting forward policy proposals with right-wing appeal.

The Sunday Times reported that Mr Cameron and senior ministers were working on plans to limit new immigrants' access to the taxpayer-funded National Health Service, which currently offers free healthcare to everyone living in Britain.

The Sunday Telegraph and the Mail on Sunday reported that senior Conservative ministers also want the party to pledge that if it wins the 2015 election it will reduce or cancel the power of the European Court of Human Rights (ECHR) to rule on British cases.