LONDON, Sept 30 (Reuters) - Sterling edged up on Friday but was on track for a fifth consecutive quarter of losses against the dollar - the currency's worst run since 1984.
The pound plunged to a 31-year low after Britain voted to leave the European Union, falling as low as $1.28 early in the third quarter, having already weakened in the run-up to the June referendum on worries about its outcome.
Sterling is now trading more than 40 U.S. cents - or 25 percent - lower than the six-year highs it reached in mid-2014, with uncertainty over Brexit and a drying-up of expectations for the Bank of England having weighed.
Last month the BoE cut its key interest rate to another record low and relaunched an asset-purchase programme in an effort to cushion the blow dealt by the referendum outcome, and some expect it to ease policy again before the end of the year.
Data showing Britain's giant services sector grew much more strongly than expected in July, in the clearest sign to date that the economy did not slow sharply after the shock of the referendum, lifted sterling only briefly, and by 1500 it flat on the day below $1.30.
After a media report said an agreement between Deutsche Bank and U.S. authorities was being discussed - which would slash huge fines over alleged misselling - sterling jumped to a day's high of $1.3024. But it was still down 1 percent for the month, and more than 2 percent down over the quarter.
"From where we're sitting today, sterling remains a pretty vulnerable currency," said Rabobank currency strategist Jane Foley. "There does seem to be an appetite now to sell into rallies, and I think that does highlight the market's sensitivity to the political uncertainty the UK faces."
"We're all very much aware of the fact that Brexit hasn't begun yet. All we've had in the referendum, and we've still got to do all the hard work," she added.
A survey published earlier on Friday showed British consumer morale rocketed back to pre-Brexit levels in September, confounding expectations that the vote to leave the EU would wreak more lasting damage on Britons' willingness to spend.
"The good news is that from the perspective of UK consumers, the Brexit shock has been fleeting," wrote Bank of Tokyo-Mitsubishi UFJ currency strategist Derek Halpenny.
Against the euro, sterling edged up 0.1 percent to 86.42 pence, but for the quarter was down more than 3 percent against the single currency.
Next week, manufacturing and production data should provide indicators of the health of the British economy. (Editing by Dominic Evans and Angus MacSwan)