* Graphic: World FX rates in 2019 http://tmsnrt.rs/2egbfVh
* Graphic: Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv (Updates after PMI numbers)
LONDON, Oct 3 (Reuters) - Sterling was little moved on Thursday despite a surprise contraction in the services sector as investors waited to receive a formal European Union response to Britain's latest Brexit offer.
The pound has found little direction in recent days, and is back where it was at the start of the week.
Britain's economy appears to have tipped into recession, according to a survey. September's IHS Markit/CIPS services Purchasing Managers' Index fell by more than any economist predicted in a Reuters poll, tumbling to a six-month low of 49.5, below the 50 level that divides growth from contraction.
The pound, however, managed a small rise and was last up 0.1% at $1.2315.
Against the euro it was up 0.1% at 89.00 pence.
Analysts say the market is largely sceptical that the EU will agree to Britain's latest offer to avoid a no-deal departure from the European Union on Oct. 31. But with hedge funds covering some of their short bets against the pound, the currency has held at current levels.
A European Parliament Brexit group believes the new proposals "do not represent a basis for an agreement", according to the draft of a statement seen by Reuters ahead of release later in the day.
"It would be one monumental climbdown by the EU to go from a customs union backstop for either the whole of the UK or Northern Ireland with no time limit to a plan that does not entail a customs union and requires some form of border checks that has a potential rolling four-year time-limit attached," MUFG analysts said in a note.
"But for now, the hope of some breakthrough may continue to provide GBP support, but we don't see it lasting... We see building risks to the downside and expect the September lows to be tested pretty quickly in the coming days/weeks," they said, referring to the $1.1959 three-year low hit in early September.
Should the EU reject Britain's Brexit proposal, attention will turn to the "Benn bill" that compels the government by Oct. 19 to seek an extension to Brexit until Jan. 31, 2020, if no deal is reached during an EU summit on Oct. 17 and 18.
But British Prime Minister Boris Johnson again told his Conservative Party at their annual conference on Wednesday that Britain would leave the EU on Oct. 31 with or without a deal.
Sterling had enjoyed a strong rally in late September as investors bet that lawmakers would be able to stop a no-deal exit.
"For me the risk-free buying opportunity comes when the Benn bill is followed through with and the ball is in the EU's court - the risk of them rejecting an extension is arguably too small for an extension not to be a given," said Simon Harvey, an FX analyst at Monex Europe. (Reporting by Tommy Wilkes; Editing by Hugh Lawson and Angus MacSwan)