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* FTSE 100 up 2.3 pct at close
* Best three-day run since 2009
* BOE's Carney's comments boost UK shares
* RBS sinks on downgrade (Recasts, adds detail and updates prices at close)
By Kit Rees and Alistair Smout
LONDON, June 30 (Reuters) - Britain's top share index closedon Thursday at its highest level for 2016, having completelyrebounded from a substantial sell-off in the wake of thecountry's vote to leave the EU.
Despite turmoil in the markets following the referendum aweek ago, Britain's FTSE 100 index ended June up 4.4percent for the month, its biggest monthly gain since October. It was helped by strength in its commodity sector and stockswith international exposure.
Comments by Bank of England Governor Mark Carney that the central bank would probably need to pump more stimulus intoBritain's economy over the summer boosted the blue chip index.
The FTSE 100 was up 2.3 percent at 6,504.33 points at itsclose. It has seen its best three-day run since April 2009, arise of almost 9 percent.
Last Thursday, the day of the referendum, the index hadclosed at 6,338.10, but it then slumped as much as 8.7 percentat the start of trading on June 24 after Britain voted to leavethe EU.
TARGET CUT
Strategists at UBS cut their end of year target for theindex to 5,500 from 6,500, citing increased politicaluncertainty after Prime Minister David Cameron said he wouldresign without invoking Article 50 to formally start the processof leaving the EU, sparking a leadership battle in rhe rulingConservative party.
"We see a significant amount of uncertainty around the UKover the next few months. We do not know who the Prime Ministerwill be, or when, or if, Article 50 is invoked, and there areeven possibilities of a General Election given the currentfluidity of UK politics," the strategists said in a note.
Royal Bank of Scotland, down around 30 percent sincethe vote to leave the EU, fell another 4.8 percent on Thursdayafter it was cut to "equal weight" from "overweight" by MorganStanley.
"A prolonged, convoluted and costly Brexit will weigh onbank earnings - particularly through lower rates & volumes,"analysts at Morgan Stanley said in a note. "For RBS, the netprofit impact is higher owing to higher operating leverage."
However, 3i Group rallied 8.5 percent after it saidit had no plans to dispose of its investment in Dutch discountretailer Action despite a number of approaches.
Sectors that earn revenues in dollars have benefited fromsterling weakness since the vote, with a rally in oil priceshelping the heavily weighted commodity sector.
Mining companies Antofagasta, Anglo American and Glencore gained between 4.2 percent and 5.1 percent as the price of copper rose.
The mid-cap FTSE 250 also gained, up 1.5 percent. Itis still down around 6 percent over the last week, as it is moreexposed to uncertainty in the domestic economy than theblue-chip FTSE 100.
Confidence among British consumers fell sharply in the daysafter the country decided to leave the EU, according to asurvey. (Reporting by Alistair Smout; Editing by Mark Trevelyan)
