(Adds Hammond comments to BBC, background)
LONDON, Nov 19 (Reuters) - British finance minister Philip Hammond, under pressure to help weakened Prime Minister Theresa May in this week's budget, promised to speed up house building and said he had some room to help voters despite his squeeze on public finances.
Aware that to some her government looks overwhelmed by the task of delivering Brexit, May needs her finance minister to show voters that she has a handle on Britain's domestic problems like a housing shortage, low productivity and stagnant pay.
Hammond told the Sunday Times he wanted 300,000 homes built each year, a big step up from recent levels closer to 200,000.
May - who suffered a rebuke from voters in an election in June when she lost her parliamentary majority - has said she wants to help younger households, many of whom fear they will not achieve the living standards of their parents' generation.
Hammond told the newspaper he would do "whatever it takes," including new powers and planning rules, to get companies to build more homes and pledged that "the next generation will have the same opportunities as their parents to own a home."
He also said the world's fifth-biggest economy was at a turning point after a hard year in what seemed to be an attempt to challenge his critics in the Conservative Party who say he is too downbeat about Britain's prospects as it prepares to leave the European Union.
Some Conservatives have even called on May to sack Hammond because he is too cautious about Britain's Brexit strategy.
Hammond said Britain was now "on the brink of making some serious progress" on Brexit and inflation looked likely to fall after rising sharply because of the fall in the value of the pound after the June 2016 Brexit vote.
"And after many years of struggling to get the (budget) deficit down and seeing our debt still rising I think we are at last about to turn that corner and see debt begin to fall," Hammond said.
Debt is expected to reach nearly 90 percent of GDP next year, more than double its levels before the global financial crisis, before falling back, according to Britain's official budget forecasters.
New forecasts are due to be delivered on Wednesday, alongside Hammond's budget.
'KINDNESS OF STRANGERS'
Britain's high debt levels have alarmed some investors and Bank of England Governor Mark Carney says the country remains dependent on "the kindness of strangers" to finance itself.
Hammond has previously set himself a target of bringing the ratio down by the end of the decade.
That target may be made easier by a move to shift debt held by housing associations off the government's books which was announced last week.
As well as his push to speed up house building, the Sunday Times said Hammond suggested he would boost spending for Britain's health service and further ease a squeeze on the pay of public sector workers in his budget plan.
But Hammond said he had to "signal a continued commitment to fiscal responsibility," suggesting he would stick to his targets for cutting the budget deficit.
"We are heavily constrained fiscally. We dont have huge amounts of room for manoeuvre. But we do have some room," he told the newspaper.
In an apparent joke at the tough balancing act he faces, Hammond was photographed by the Sunday Times looking puzzled and scratching his head as he pored over papers coming from his famous red budget briefcase.
Many economists say Hammond will struggle to meet his target of eliminating Britain's budget deficit by the mid-2020s because of the country's stubborn productivity problem.
Britain's official budget forecasters have said they expect to cut their productivity growth forecasts, suggesting slower overall economic growth ahead and less tax revenue for Hammond.
($1 = 0.7569 pounds) (Writing by William Schomberg; Editing by Mark Potter)