(Updates prices, adds quote) * Sterling falls against euro, rises versus dollar * Euro rebounds from falls on Thursday after ECB * UK services PMI weaker than expected * Economy concerns may still weigh on sterling By Jessica Mortimer LONDON, Aug 3 (Reuters) - Sterling fell to a three-week low against a firmer euro on Friday, with markets turning more optimistic about the prospect of future intervention by the European Central Bank to lower sky-high Spanish and Italian borrowing costs. The euro rose 0.7 percent to 79.135 pence, its strongest since July 13 and was on course for its biggest weekly gain since late February. The single currency rebounded from steep losses the previous day suffered on disappointment after the European Central Bank took no immediate action to tackle the euro zone debt crisis. But a reassessment on Friday left traders questioning whether the euro's falls may have been overdone "It looks like the market is changing its mind on the ECB yesterday and that is supporting euro/sterling," said John Hardy, head of currency strategy at Saxo. "The initial disappointment was that nothing was coming right now but now people are thinking that maybe something is afoot anyway." The ECB said on Thursday it may resume its programme of buying the government bonds of indebted euro zone countries, though markets were disappointed by the conditions it set and by concerns about opposition from Germany. Sterling gained against the dollar, however, tracking gains in equities and riskier currencies after better-than-expected U.S. jobs and manufacturing data. Sterling was up 0.5 percent at $1.5595, rebounding well above a low of $1.5490 hit on Thursday. UK ECONOMY The pound shrugged off figures on Friday showing growth in Britain's dominant services sector slowed more than expected in July, casting doubt over whether the economy can rebound after three consecutive quarters of contraction. Traders said many in the market had feared an even worse result after an equivalent survey on manufacturing earlier this week showed that sector shrank at its fastest pace in nearly three years. Nevertheless, concerns about the UK have been growing since recent data showed the UK economy slumped in the second quarter, marking its third consecutive quarterly contraction. "The expectations are that the economy will rebound modestly in the third quarter but that doesn't change the picture of growth stagnating," said Lee Hardman, currency economist at BTMU. "A weak growth outlook and the likelihood of more monetary easing is still a negative for sterling." The Bank of England left interest rates and its quantitative easing target unchanged on Thursday but expectations are growing that the central bank will opt for further monetary easing in the coming months to aid a flagging economy. (editing by Ron Askew)

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