LONDON (Reuters) - Britain's service sector grew much faster than expected in May, with new business increasing at its fastest rate in over three years, a survey showed on Wednesday, showing that the economy is picking up speed.

The Purchasing Managers' Index (PMI) for services, produced by Markit and the Chartered Institute of Purchasing and Supply, rose to 54.9 in May from 52.9 in April.

That was the strongest reading since March 2012, and easily beat the top forecast of 53.6 in a Reuters poll of 30 economists. The median forecast was 53.0.

The figure was helped by better weather and was boosted by a rise in new orders, which hit their highest level since February 2010.

"The UK economy has moved up a gear with all cylinders now firing," said economist Chris Williamson from Markit.

Added to positive manufacturing and construction PMI surveys this week, the figures suggested economic growth was gaining speed in the second quarter, and could reach 0.5 per cent if June sees a sustained expansion, added Mr Williamson.

Britain's economy grew 0.3 per cent in the first three months of 2013, avoiding a return to recession.

The strong service sector reading will bring relief to Finance Minister George Osborne, who has faced criticism at home and from the International Monetary Fund for his austerity programme.

It also reinforces expectations that the Bank of England will refrain from further bond buying to stimulate the economy.

The central bank holds its June policy meeting on Wednesday and Thursday, the last before Sir Mervyn King is replaced by Mark Carney as governor on July 1.

"New governor Mark Carney will have the benefit of taking the reins of an economy that is already showing signs of acquiring 'escape velocity' from the doldrums it has been wallowing in for much of the last two years," said Mr Williamson.

"The increasingly buoyant picture and improved outlook painted by the PMIs effectively kills off any chance of the Bank of England's Monetary Policy Committee voting for more stimulus such as asset purchases for the foreseeable future."