* Graphic: sterling and gilt yields http://bit.ly/2dgAXn1
* Graphic: World FX rates in 2017 http://tmsnrt.rs/2egbfVh
* Graphic: Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv
LONDON, Oct 4 (Reuters) - Sterling rebounded on Wednesday from a three-week low as a survey of Britain's dominant services sector showed growth sped up unexpectedly last month, raising expectations the Bank of England will hike interest rates in November.
Futures markets expect almost two rate increases over the next one year, a sharp turnaround from recent months after the Bank of England struck an optimistic note about the outlook for the British economy. Rates have been unchanged since 2009.
A senior currency strategist at a European bank in London expects the outlook for interest rates to be a key driver for sterling in the coming months rather than a November rate increase as that has already been priced into financial markets.
"What's going to matter is the signaling for the currency, hiking once, considering it could hike again and keeping that language for the market," the strategist said.
The monthly purchasing managers' index (PMI) for the services sector picked up to 53.6 in September, slightly better than expectations in a Reuters poll of economists, and easily above the 50 level that separates growth from contraction.
Sterling climbed 0.3 percent to $1.3270, just shy of the day's highs and moving further away from a three-week low of $1.3222 in the previous session. Against the euro , the pound was a shade stronger at 88.63 pence.
"While the short-term risks to demand since the Brexit vote have not materialised in a serious way, the UK economy should be faring much better today on the back of the ongoing global upswing," said Kallum Pickering, senior UK economist at Berenberg in London, who expects a rate increase in November.
Some of the optimism surrounding sterling after the data was punctured by comments from ratings agency Standard & Poor's, which said it was "a bit sceptical" about the notion that Britain's economy needed an interest rate increase.
Uncertainty about the outcome of the negotiations on Britain's divorce from the EU dragged sterling down to three-week lows in the previous session. It has fallen more than 10 percent against the dollar since Britain's June 2016 EU referendum in which a narrow majority voted to leave the bloc.
Brexit minister David Davis told the conference of the governing Conservative Party on Tuesday that Britain wanted to negotiate an exit agreement but was prepared to walk away with no deal.
In her keynote speech to the conference on Wednesday, which had no immediate impact on the currency market, Prime Minister Theresa May said she was confident of getting a deal that would work for both sides. (Reporting by Saikat Chatterjee and Fanny Potkin; editing by Mark Heinrich)