* Sterling rises versus dollar as equities, euro gain * But still vulnerable, stays near 2-1/2 week low * Pound weak versus euro, just shy of 80 pence FREE GUIDES AND REPORTS FROM DIANOMIADVERTISEMENT House Prices Report Why UK House Prices Look Set to Collapse Download FREE Report * UK construction PMI weaker than expected By Jessica Mortimer LONDON, Oct 2 (Reuters) - Sterling edged up against a weaker dollar on Tuesday, helped by gains in the euro and in equities, but it was vulnerable to renewed falls and weak against the euro as data highlighted UK economic fragility. Figures on Tuesday showed construction activity fell for a second straight month in September. The purchasing managers' index rose to 49.5 from 49.0 but was below forecasts and below the 50 mark, signalling contraction. It followed a weak manufacturing PMI survey on Monday, as well as poor mortgage lending data and a Nationwide survey on Tuesday revealing a fall in house prices. This dampened recent optimism that the UK economy may have enjoyed a decent recovery in the third quarter. The pound was up 0.1 percent against the dollar at $1.6140, off a two-and-a-half week low of $1.6109 hit on Monday, with traders saying a reported options expiry later at $1.6150 may influence trade and keep it close to that level. Talk that Spain is on course to request a bailout soon lifted the euro and equity markets, supporting the pound. Spain must apply for aid in order for the European Central Bank to implement a plan to buy its bonds and bring down its borrowing costs. "Euro/dollar may push higher, which will pull sterling/dollar up," said Paul Robson, currency strategist at RBS, though he said this would also mean the pound would fall versus the euro. He said the euro may rise to 82-83 pence in coming weeks. The euro was up 0.2 percent on the day at 80.02 pence , pursuing a strong recovery from last week's three-week low of 79.23 pence. A break above the Sept. 21 high of 80.08 pence and reported stop loss buy orders above 80.10 pence could trigger more gains for the shared currency. GAINS LIMITED VERSUS DOLLAR Most economists estimate that the economy returned to growth in the three months to September after three quarters of contraction, though the recovery is expected to be muted and this may hamper the pound. "Cable (sterling/dollar) is still vulnerable to the downside and could fall to $1.59 within the next week or two," said Michael Derks, chief strategist at FXPro. Traders reported offers at $1.6175, just above the 100-hour moving average at $1.6173, and analysts said the pound remained on a downward trend since hitting a 13-month peak of $1.6310 last month. "The data yesterday was not particularly friendly, Nationwide house price numbers were on the softer side ... The underlying message is that the economy is generally fairly moribund," Derks said. PMI surveys this week on manufacturing, construction and finally services - due on Wednesday - are giving investors a gauge of third quarter performance. The British Chambers of Commerce predicted growth of 0.5 percent in the third quarter on Tuesday but said the economy has lost momentum, with firms scaling back investment and hiring plans. "The UK might get a decent third quarter, but that would only be payback for a very weak two quarters before that," RBS' Robson said.

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