UPDATE 1-BP siphoning off 40 pct of Gulf of Mexico oil leak

* Oil spill costs it $625 million so far, vs $450 mln May 13

* Siphon tube collecting 2,000 barrels a day, up from 1,000

* 15,600 claims filed, 2,700 have already been paid (Adds detail)

LONDON, May 18 (Reuters) - BP Plc (BP.L) doubled the estimate of how much oil it was managing to siphon from the leak in the Gulf of Mexico, as it lifted the total bill for the clean-up to $625 million.

BP said on Tuesday its "quick fix" mile-long siphon tube deployed on the leaking well was now collecting 40 percent of the estimated 5,000 barrels of oil flowing into the sea per day, double the 1,000 barrels it was capturing on Monday.

The updated cost of the oil spill was $175 million more than the oil major reported five days ago and includes the spill response, containment, relief well drilling, grants to the Gulf Coast States, settlements and federal costs. [ID:nLDE64C0I9]

BP shares were up 0.7 percent to 533.6 pence at 0811 GMT, mirroring a 0.8 percent rise in the FTSE 100 .FTSE.

"The costs were always going to go up," said Panmure Gordon analyst Peter Hitchens, who believes the costs could top $2 billion. "They are managing to get about 2,000 barrels a day and hopefully get that higher ... which means there is less oil floating to the surface which is good news."

Analyst forecasts for the clean-up costs and compensation for the spill off the coast of Louisiana have ranged from a few hundred million dollars to over $12 billion.

The company also said 15,600 claims have been filed, more than double the 6,700 filed by last Thursday, of which 2,700 have already been paid.

Investors have knocked around $30 billion off BP's stock market value over the spill, which followed an April 20 rig explosion that killed 11 workers. (Reporting by Sarah Young; Editing by David Holmes)