* UK faces choice of deeper cuts or longer austerity
* PM Cameron says will not waver from cutting deficit
* Cameron appeals to powerful anti-EU Conservatives
* Labour leads Cameron's party by 10 percentage points in polls
(Adds quotes, details) By Guy Faulconbridge and Matt Falloon
BIRMINGHAM, England, Oct 7 (Reuters) - Britain will have to keep cutting public spending to reduce the budget deficit, Prime Minister David Cameron said on Sunday, underlining the government's tough task of trying to shunt the economy out of recession and winning back waning public support.
An aide said the government was paving the way for the next phase of austerity rather than signalling bigger than planned cuts, but investors say longer or deeper cuts look likely after a return to recession cast doubt over Britain's deficit targets.
The 2015 election will be fought on the state of the economy and how best to get the deficit under control. The Conservative-led coalition government planned to all but erase the deficit by 2015 but has already been forced to add two more years of cuts.
Underlying borrowing between April and August was a fifth higher than last year, suggesting either bigger cuts or a further extension of austerity could be on the cards when the government updates its economic forecasts on Dec. 5.
"It is a very challenging situation, you only have to switch on your television set and look at what is happening in the euro zone. We have got many countries going into quite a deep recession, these are very difficult times," Cameron said.
"We inherited a budget deficit at around 11 percent, it is down to eight percent," he told the BBC. "The figures for this year, it is too early to say where they will end up."
Official forecasts in March predicted a fall to below six percent this year, a target which now looks uncertain.
Abandoning the austerity plan would prove politically disastrous for the Conservatives, who staked their 2010 election pitch on it.
"The economy is healing. But it's a longer and harder road that we have to travel down," finance minister George Osborne said in an interview with the Mail on Sunday. "There will have to be further cuts."
COALITION TENSIONS
The Labour opposition has pulled ahead of Cameron's party due to public unease with the austerity drive, while support has dived for the Liberal Democrats junior coalition partners.
Pollsters say Cameron will struggle to win an outright majority in 2015 unless the economy bounces back and the austerity plan starts to bear fruit.
Labour and the Lib Dems want to see the wealthy make a bigger contribution to reducing government borrowing.
But the Conservatives dismissed the idea of a tax on the wealthy - such as on expensive homes - and called for more cuts in welfare spending, comments likely to create further tension in an already uneasy coalition government.
In an effort to woo back middle class voters, Cameron also announced a freeze in a tax that pays for local services and a cap on rail fare increases.
"If we want to avoid cuts in things like hospitals and schools and the services that we all rely on, we have to look at things like the welfare budget, where we are still spending as a country 80 billion pounds on working age welfare," he said.
"We've capped welfare but we need to go further."
Beyond the economy, Cameron also faces problems in his centre-right party, with some arguing he has not taken a tough enough line on Europe and a few calling for a new leader, such as Boris Johnson, the popular Conservative London Mayor.
To pacify the anti-EU wing of his party, Cameron threatened to use Britain's veto if the 27-nation bloc seeks to inflate its 2014-2020 budget.
He suggested the EU should at some point split its budget into two - one for the euro zone and one for the countries outside the common currency, including Britain.
Cameron, much to the delight of the anti-EU wing, used the veto last year to keep Britain out of a European fiscal and economic pact aimed at resolving the euro zone debt crisis.
"People in Europe know I mean what I say. I sat round that table - 27 countries, 26 of them signing up to a treaty - and I said this is not in Britain's interest," he said.
"I don't care how much pressure you put on, I'm not signing, we are not having it. They know what I am capable of saying, no, and if I don't get a good deal I'll say no again."
(Additional reporting by Tim Castle; Writing by David Stamp and Matt Falloon; Editing by Jon Hemming)
((matt.falloon@thomsonreuters.com))
Keywords: BRITAIN POLITICS/