By William Schomberg

LONDON, Nov 25 (Reuters) - British finance minister George Osborne will renew his push to fix the country's public finances on Wednesday, taking a gamble that voters can accept four more years of deep spending cuts.

Osborne, a contender to succeed David Cameron as prime minister, is expected to tell parliament he is still aiming for a budget surplus by the end of the decade, which could allow him to deliver income tax cuts promised before May's election.

But the size of the projected surplus is likely to be revised down after one of his most controversial savings ideas -- big cuts to tax credits for low-earning households -- was blocked in a rare rebellion by Britain's upper house last month.

Osborne has largely stuck to his guns and cut spending in many areas of government in order to bring down the huge deficit he inherited in 2010. He endured deep unpopularity until the economy picked up in 2013.

Osborne originally intended to have eliminated the deficit by now but has only managed to halve it. At nearly 5 percent of economic output in the last financial year, he says it still poses a real threat to Britain's economic security.

"If our country doesn't bring the deficit down, the deficit could bring our country down again," he said earlier this month.

Osborne wants to cut government departmental spending to under 17 percent of economic output by the end of the decade, its lowest share since at least 1999, according to the Institute for Fiscal Studies, a non-partisan think tank.

As in the first five years of his austerity push, he plans to protect Britain's health service, schools and foreign aid from cuts, and he plans to boost defence spending.

That means the cuts to be announced on Wednesday will be all the deeper for other, unprotected, areas such as policing.

The prospect of major job losses among police has alarmed some senior officers who are worried about how they would respond to a Paris-style attack in Britain.

Town halls are also bracing for more cuts which could affect services that many people rely on, such as rubbish collection and social care for the elderly and children, local government officials have warned.

Some unprotected government departments could see their budgets slashed by 50 percent over the decade to 2020.

At the same time, Osborne is expected to say he will phase in the introduction of the tax credit cuts that provoked outrage when he first announced the idea in July.

Many economists say Osborne's insistence on a budget surplus had more to do with scoring political points over the Labour opposition party before May's elections than economics.