* FTSE 100 down 0.2 pct at close
* Sterling climbs off lows
* Provident shares sink on Moneybarn investigation
* Tesco leads gainers after upgrade (Recasts, adds details and updates prices at close)
LONDON, Dec 5 (Reuters) - Britain's main share index gave up early gains on Tuesday to close slightly lower, as sterling picked itself up from a session low on the back of timid optimism about a Brexit deal.
The blue chip FTSE 100 index ended the session 0.2 percent lower at 7,327.50 points, joining the pan-European STOXX index in negative territory.
While a weaker pound initially supported the index, the currency later cut losses to trade just slightly lower, which put pressure on Britain's blue chips.
With no certainty over whether the UK and the European Union will be able to make a breakthrough on a divorce settlement, the pound is likely to continue to fluctuate and weigh on shares.
"Fluctuations in the pound exchange rates were only a first taste of what is to come," Commerzbank said in a note.
The fall in sterling since the June 2016 Brexit vote has given an accounting boost to UK blue chips with revenues in dollars, and a weak pound typically supports the FTSE.
Elsewhere, supermarkets were by far the best FTSE performers, with Tesco and Sainsbury rising by 3 percent and 2.7 percent respectively.
Goldman Sachs raised its rating for Tesco to "buy" and said margin pressure in the UK grocery market was easing.
Yet falls among cyclical stocks, such as financials and miners, kept broader gains in check.
A drop in base metals prices kept mining stocks in negative territory, with investors locking in profits on recent gains in nickel and copper.
Anglo American, Antofagasta, Glencore and Rio Tinto fell between 1.7 percent and 2.5 percent.
However, Standard Chartered, with a 3 percent rise, was the top gainer after JP Morgan raised its rating and included the stock in its EU bank top picks list.
British lender Provident Financial's shares dropped more than 10 percent after the UK financial watchdog opened an investigation into Moneybarn, its car and van financing arm.
British movie theater operator Cineworld Group Plc lost 3.7 percent after it said it reached an agreement to buy U.S. peer Regal Entertainment Group for $3.6 billion.
(Reporting by Julien Ponthus and Kit Rees; editing by Alexander Smith)