* UK GDP growth cut for every year up to early 2020s
* Deficit forecasts cut in short term, wider later on
* Under-fire Hammond to spend on housing, health, Brexit
* Sterling falls before picking up (Adds comments from IFS's Johnson)
By William Schomberg, David Milliken and William James
LONDON, Nov 22 (Reuters) - Brexit-bound Britain slashed its economic growth forecasts and ramped up its borrowing plans going into the 2020s, but finance minister Philip Hammond announced a number of spending steps aimed at winning back voters.
Hammond was under heavy pressure to use his budget statement on Wednesday to turn around the fortunes of Prime Minister Theresa May. Some lawmakers, still smarting from an election mauling in June, had even called on May to fire him for his cautious approach to Brexit and to the public finances.
But Hammond looked relaxed and cracked jokes as he said he would offer help to voters by abolishing a property purchase tax for 80 percent of first-time home-buyers, keeping a freeze on fuel duty and spending more on the health service.
He also committed 44 billion pounds ($58 billion) - 15 billion of it new money - over five years to deliver 300,000 new homes a year by the mid-2020s, addressing Britain's acute housing shortage.
After Brexit supporters criticised him for starving ministers of funds to prepare for leaving the EU, he earmarked an extra 3 billion pounds for Brexit readiness.
Hammond said he was sticking to the Conservatives' priority since coming to power in 2010 of fixing the public finances.
"We took over an economy with the highest budget deficit in our peacetime history," he told parliament.
"Since then, thanks to the hard work of the British people, that deficit has been shrinking and next year will be below 2 percent. But our debt is still too high," he said.
Despite that message, Britain's official budget watchdog said the spending plans for the next two years were a "significant giveaway".
Britain is set to borrow 29.1 billion pounds more by the end of the 2021/22 tax year than it expected eight months ago.
"The chancellor has been bolder than widely expected and has bowed to pressure to ease the near-term pace of the fiscal consolidation," Samuel Tombs, an economist with Pantheon Macroeconomics, said.
Sterling initially fell as Hammond announced the gloomy forecasts for the economy - which contrast with stronger growth in many other rich nations - but rose later to hit a three-week high against the U.S. dollar.
At a time when inflation has risen sharply and wages have grown only slowly, many voters are angry about years of spending cuts to certain public services.
"We understand the frustration of families where real incomes are under pressure," Hammond said, promising to reduce the delays in receiving benefit payments that many families have suffered under changes to the welfare system.
He also sought to help businesses by slowing the rise in the so-called business rates tax on the premises they occupy, and he raised a tax credit for research and development.
But the limitations on Hammond were clear as he said the war chest he is keeping in reserve to help the economy - and possibly the Conservatives before the next election due by 2022 - had almost halved in size to 14.8 billion pounds, with most of the hit coming from the lower growth forecasts.
Britain's budget forecasters now expect gross domestic product will grow by 1.5 percent in 2017, compared with a forecast of 2.0 percent made in March, reflecting a slowdown this year as the Brexit vote weighed.
The Office for Budget Responsibility also cut its GDP growth forecasts in 2019 and 2020 to 1.3 percent in both years, down from 1.7 and 1.9 percent previously. For 2021 and 2022, economic growth was still seen weak at 1.5 and 1.6 percent respectively.
"There is a recognition from the OBR that the growth outlook is dire at a time when the world economy is enjoying a synchronised upswing. Germany is enjoying a boom and even Italy is growing faster than the UK," Daiwa Capital Markets Europe's Chris Scicluna said.
The OBR's gloomier view on growth was based largely on a cut to its projections for productivity, the Achilles heel of Britain's economy since the global financial crisis, due to shortfalls in skills training and infrastructure.
"The persistence of weak productivity growth does not bode well for the UK's growth potential in the years ahead," it said.
The OBR now expected Britain would borrow less this year and next but more in the following years as the slowdown in the economy bites.
The projected budget deficit of 1.3 percent of GDP in the 2021/22 financial year was almost double the previous estimate.
Paul Johnson, director of the Institute for Fiscal Studies, said Hammond's target of eliminating the budget deficit by the middle of the next decade seemed increasingly hard. "That looks really pretty tough and unlikely to me now," he said.
Before last year's Brexit vote, Britain had been aiming to post a budget surplus by the end of this decade, itself a delay from an original target of fixing the public finances by 2015.
There was some better news for the public finances - Britain's debt was expected to peak at 86.4 percent of GDP this year - about double its level before the global financial crisis - before falling in the coming years.
But the OBR forecasters linked the fall largely to the sale of shares in state-run bank RBS and an accounting switch to get housing association debt off the government's books. ($1 = 0.7526 pounds)
Reporting by William Schomberg, David Milliken and William James; Additional reporting by Andy Bruce and UK bureau; Writing by William Schomberg; Editing by Hugh Lawson