* FTSE 100 up 0.6 pct
* U.S. Senate leaders talk of "tremendous progress" on deal
* Miners rise as Rio boosts forecast copper output
* Burberry falls after losing CEO to Apple (Updates prices, adds quotes, detail)
By Alistair Smout
LONDON, Oct 15 Britain's top share index rose to its highest level so far in October on Tuesday, buoyed by signs of a deal to fix the U.S. budget and debt ceiling stalemate that has weighed on stock markets this month.
Miners and banks were lifted after U.S. Senate Majority Leader Harry Reid, a Democrat, said Senate leaders had made "tremendous progress" on working towards a deal to avoid default after a day of talks with his Republican counterpart Mitch McConnell on Monday.
U.S. senators expressed hope that a bipartisan deal could emerge on Tuesday to end Washington's fiscal crisis even as Republicans in the House of Representatives said they were working on a separate plan.
"The market is coming around to the idea that the 17th is not a hard deadline, and there seems to have been progress towards a resolution," said James Butterfill, global equity strategist at Coutts.
"We're rallying already on hopes for a deal ... There may not be much room for another relief rally. My target for the FTSE is 6,550, and we're very close to that, so there isn't a significant amount of upside left."
The blue-chip FTSE 100 index rose by 0.6 percent, or 40.10 points, to 6,547.75 points by 1449 GMT, having hit its highest since September 27, which was before the political deadlock that partially shut down the U.S. government.
Concerns that the United States will hit the $16.7 trillion U.S. debt ceiling on Oct. 17 have weighed on markets since the beginning of the month, when political deadlock began a partial shutdown of the federal government.
Stocks sensitive to optimism over the global economy were the biggest gainers, with financials and basic material stocks combining to add more than 2 points to the index.
Miner Rio Tinto gained 3.9 percent, a top FTSE riser, and added the most points to the FTSE 100 after posting record coal and iron ore output in the third quarter and boosting its forecast copper output for 2013.
But Burberry missed out on the FTSE 100's rally, slumping 6.1 percent to make it the worst-performing FTSE stock after the group lost its CEO to technology and mobile phone group Apple.
Traders said the loss of CEO Angela Ahrendts marked another negative drag on the stock, which had already lost ground last week after warning of a slowdown in its important Chinese market.
"Burberry have had an unbelievable performance in what you might think would have been a difficult few years for a company like theirs ... And that good performance has been partly as a result of strong leadership," IG sales trader Will Hedden said.
"They may not start struggling as a company overnight, but in the long run it could definitely have an effect."
(Editing by Catherine Evans)