* Sterling falls to 10-day low vs dollar of $1.5786 * Dollar firmer on worries about China growth, Greece * Focus on UK services PMI at 0928 GMT * Euro steady vs sterling but stays weak LONDON, March 5 (Reuters) - Sterling fell to a 10-day low against the dollar on Monday as uncertainty surrounding Greece's bailout and concerns about growth in China weighed on riskier assets, while investors awaited UK services sector data. The purchasing managers' survey on services, which is key to the UK economy, is expected to dip to 54.9 in February from a very solid 56.0 in January, and a weaker number may pressure the pound further, although recent data have suggested the economy is recovering. Sterling was down 0.2 percent at $1.5801 against the dollar , having broken below reported stop-loss sell orders to hit $1.5786, its weakest since Feb. 24. Charts pointed to a weaker outlook for sterling versus the dollar after it broke and closed below its 200-day moving average around $1.5892 on Friday. "There is nothing really sterling specific driving the market. The euro broke below $1.32, which gave the dollar a general modest lift and there has been a risk-off theme in London trade," said Derek Halpenny, European head of currency research at Bank of Tokyo-Mitsubishi. "Services PMI has quite a good correlation with real GDP and if it were to surprise more significantly to the downside or the upside it would trigger a reaction in sterling". More falls could see the pound target its 100-week moving average around $1.5778, though traders cited bids just below there that may prop it up, then the 100-day moving average at $1.5710 and the mid-February low of $1.5644. Analysts and traders said sterling was largely being driven by developments elsewhere, with the safe-haven dollar broadly supported after China cut its annual growth target, sparking worries about the global growth outlook. Concerns about risks surrounding the bailout deal for Greece also knocked sentiment, with the market focused on a deadline on Thursday for Greece to complete a bond exchange with private creditors. This was expected to keep the euro under pressure. The single currency was steady at 83.33 pence, not far from a 2-1/2-week low of 83.13 pence hit on Friday. Recent firmer UK data have helped support the pound against the euro, dampening the prospect of further quantitative easing by the Bank of England. The British Chambers of Commerce, Britain's largest business lobby group, revised down its forecast for growth this year but said Britain will avert recession this year and the BoE will not need to inject more stimulus. "The UK continues to set itself apart from the problems in Europe despite the fact that it remains one of the key export markets for goods and services," said Michael Hewson, analyst at CMC Markets. He added that the euro is approaching support around 83.00 pence from a trend line drawn from the January low at 82.22 pence. A firm break below 83.00 could target this low. (Editing by Stephen Nisbet)

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