* Services PMI beats forecasts but economy close to stagnation
* Dollar weakness helping pound as Brexit concerns dominate
* Graphic: World FX rates in 2019 http://tmsnrt.rs/2egbfVh
* Graphic: Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv (Writes through after PMI data, adds quotes)
LONDON, June 5 (Reuters) - Sterling rose to a seven-day high on Wednesday, helped by weakness in the dollar and a slightly better-than-expected reading of a closely watched survey on Britain's services sector.
With uncertainty over who the next British prime minister will be and concerns about the prospect of a no-deal Brexit, the pound has remained under pressure - it's recovery from five-month lows hit on Friday has been more to do with a selloff in the dollar than improved sentiment towards the pound.
Sterling has proven less resilient against the euro, where it remains near 5-1/2 month lows.
The IHS Markit/CIPS services Purchasing Managers' Index (PMI) edged up to 51.0 in May from 50.4 in April, its strongest reading in three months and slightly above economists' average forecast in a Reuters poll.
But the survey, combined with earlier numbers on the manufacturing and construction sectors, showed that British economic growth overall almost halted last month.
"This is far from a picture of real strength and while a modest increase in business activity and new work rising for the first time this year is positive, most of the signs continue to point to the UK economy being close to stagnation," said David Cheetham, market analyst at online broker XTB.
Sterling rose 0.1% to $1.2718 after earlier rising to $1.2723, a seven-day high.
Against the euro the pound lost 0.1% to 88.71 pence , slightly above 5-1/2 month lows.
With the Conservative party contenders to take over from Prime Minister Theresa May setting out their plans for Brexit, the pound remains at the mercy of politics, analysts say.
Britain is due to leave the European Union at the end of October but investors still do not know for certain when, how or even if the United Kingdom will leave.
Promises from U.S. President Donald Trump of a "phenomenal" post-Brexit trade deal on Tuesday did little to move the currency, as the race to replace May and Brexit dominate trading of the pound. (Reporting by Tommy Wilkes; Editing by Toby Chopra, John Stonestreet and Peter Graff)