LONDON- Sterling gave up earlier gains and briefly hit the day's lows on Wednesday at $1.3098 after the Times reported that Britain's Prime Minister Theresa May had rejected an improved offer from EU chief negotiator Michel Barnier on the Irish border issue.

May will tell EU leaders meeting in Salzburg, Austria, that any solution must be for the entire United Kingdom and that her "Chequers" proposals were designed to address this, the Times said. 

Sterling slid around more than half a cent against the dollar after the report to a low of $1.3098 before edging slightly higher to last trade at $1.313.

The pound remained well below an intraday high of $1.3215, its highest since July 17 GBP=D3 after British inflation data climbed unexpectedly to a six-month high in August. 

"The European Union goal posts are coming in but the UK government posts look not to be shifting for now," said Neil Jones, head of hedge fund sales at Mizuho based in London.

The European Union's chief Brexit negotiator Michel Barnier said on Tuesday the bloc was ready to improve its proposal for an "insurance policy" backstop arrangement on how to manage its Irish border that would avoid creating a physical customs border on the Irish Sea. 

The pound had earlier risen to a nine-week high, helped by strong UK inflation data and as investors prepared for the European Union summit where diplomats will try to pave the way for an agreement on Brexit.

Brussels and London have made positive noises in recent days on major obstacles, including how to keep an open border between the British province of Northern Ireland and EU-member Ireland, though investors have shied away from taking big bets.

That has helped sterling rally more than 4 percent from 2018 lows hit in August when fears that Britain would crash out of the EU without a trade deal spooked investors.

Wednesday's figures showed consumer price inflation rose at an annual rate of 2.7 percent in August, compared with 2.5 percent in July. 

The data may surprise Bank of England officials who last month raised interest rates for the second time since the financial crisis. The BoE last week said it expected inflation to cool to 2.4 percent in August.

(Reporting by Tom Finn and Saikat Chatterjee; Editing by Janet Lawrence) ((tom.finn@tr.com; +44 2075427508 ; Reuters Messaging: tom.finn.reuters.com@reuters.net))