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By Nia Williams

LONDON, Feb 21 (Reuters) - Sterling dipped against the safe-haven dollar on Tuesday as initial positive sentiment towards a Greek bailout deal waned, while a fragile economic outlook for the UK kept investors wary of buying the pound.

Sterling also underperformed the euro, trading within sight of a seven-week low on reported heavy selling by model funds.

Euro zone finance ministers finally approved a second bailout for Greece overnight that removed the threat of a disorderly default next month but was seen as unlikely to solve the debt-laden country's economic woes.

Sentiment towards the single currency was lukewarm amid choppy trade, supporting demand for the dollar against perceived riskier currencies including sterling. Market players also said a large sterling sell order from a European investment bank weighed on the pound.

Still, risk appetite and U.S. equity markets picked up later in the European session, boosting the euro. Analysts said the Greek deal was at least a step in the right direction.

"What came out of Greece last night was mildly positive, although there is still a long way to go and the market is cautious," said Gavin Friend, currency analyst at National Australia Bank.

The pound was down 0.2 percent on the day at $1.5811, after initial news of the Greek deal prompted it to rise to $1.5865. Resistance was at the 200-day moving average of $1.5913, together with this month's high of $1.5929.

The euro rose 0.5 percent against the pound to 83.95 pence, after earlier hitting a session high of 84.03 pence on demand from model funds, with Swiss investors also cited as buyers. Offers reported around 84.00/10 pence were expected to cap gains and stop loss orders were seen through 84.20 pence.

Analysts said 84.09 pence was a crucial level of resistance for the euro, where it has failed repeatedly since the end of December.

"A clear break of 84.10/15 and quite a few people will be looking for a move to 85 the figure," said Friend.

UK PUBLIC FINANCES BRIGHTER

Analysts played down the impact of UK public sector finance data for January that showed the biggest monthly surplus in four years and was far better than forecast.

"Britain typically brings in cash in January so this was not enough to sustain sterling," said Kathleen Brooks, research director at FOREX.com, who added sterling's performance against the dollar was mainly being driven by swings in risk sentiment.

Ratings agency Moody's put the UK's prized triple-A sovereign rating on review for a possible downgrade earlier this month, keeping the pressure on Chancellor George Osborne to stick with strict austerity measures and avoid tax cuts at next month's UK budget.

"It's a good set of data. It means that it looks like we are heading for a full year financial improvement of around 18 billion pounds," said Ross Walker, economist at RBS.

"We are still borrowing huge sums, but against a backdrop where we had Moody's negative outlook and there was growing talk about the UK's rating ... these numbers help."

Sterling's recent moves have been dominated by developments in Greece and signs of improved UK data, including better-than-expected retail sales numbers. The pound may also take cues from the minutes of the Bank of England's latest monetary policy committee meeting, due on Wednesday.

The MPC voted for another 50 billion pounds of asset purchases at its February meeting to try to stimulate the sluggish economy.

BoE Deputy Governor Charles Bean will give a speech at the Scottish Council for Development and Industry around 1930 GMT. Market players are likely to scrutinise the speech for any further hints on whether the bank would consider more asset purchasing in the months ahead.

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