Britain's FTSE ends June on 2016 high

* FTSE 100 up 2.3 pct at close

* Best three-day run since 2009

* BOE (Shenzhen: 200725.SZ - news) 's Carney's comments boost UK shares

* RBS (LSE: RBS.L - news) 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 closed on Thursday at its highest level for 2016, having completely rebounded from a substantial sell-off in the wake of the country's vote to leave the EU.

Despite turmoil in the markets following the referendum a week ago, Britain's FTSE 100 index ended June up 4.4 percent for the month, its biggest monthly gain since October. It was helped by strength in its commodity sector and stocks with international exposure.

Comments by Bank of England Governor Mark Carney that the central bank would probably need to pump more stimulus into Britain's economy over the summer boosted the blue chip index.

The FTSE 100 was up 2.3 percent at 6,504.33 points at its close. It has seen its best three-day run since April 2009, a rise of almost 9 percent.

Last Thursday, the day of the referendum, the index had closed at 6,338.10, but it then slumped as much as 8.7 percent at the start of trading on June 24 after Britain voted to leave the EU.

TARGET CUT

Strategists at UBS (LSE: 0QNR.L - news) cut their end of year target for the index to 5,500 from 6,500, citing increased political uncertainty after Prime Minister David Cameron said he would resign without invoking Article 50 to formally start the process of leaving the EU, sparking a leadership battle in rhe ruling Conservative party.

"We see a significant amount of uncertainty around the UK over the next few months. We do not know who the Prime Minister will be, or when, or if, Article 50 is invoked, and there are even possibilities of a General Election given the current fluidity of UK politics," the strategists said in a note.

Royal Bank of Scotland, down around 30 percent since the vote to leave the EU, fell another 4.8 percent on Thursday after it was cut to "equal weight" from "overweight" by Morgan Stanley.

"A prolonged, convoluted and costly Brexit will weigh on bank earnings - particularly through lower rates & volumes," analysts at Morgan Stanley (Xetra: 885836 - news) said in a note. "For RBS, the net profit impact is higher owing to higher operating leverage."

However, 3i Group rallied 8.5 percent after it said it had no plans to dispose of its investment in Dutch discount retailer Action despite a number of approaches.

Sectors that earn revenues in dollars have benefited from sterling weakness since the vote, with a rally in oil prices helping the heavily weighted commodity sector.

Mining companies Antofagasta (Other OTC: ANFGF - news) , Anglo American (LSE: AAL.L - news) and Glencore (Xetra: A1JAGV - news) 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. It is still down around 6 percent over the last week, as it is more exposed to uncertainty in the domestic economy than the blue-chip FTSE 100.

Confidence among British consumers fell sharply in the days after the country decided to leave the EU, according to a survey. (Reporting by Alistair Smout; Editing by Mark Trevelyan)