* More upbeat Asian sentiment supports oil
* Physical oil overhang remains in place
* Mexico says it can not cut output, British production to rise
* End of summer driving season to lower U.S. demand (Changes dateline, previous SINGAPORE, updates throughout)
By Libby George
LONDON, Sept 9 (Reuters) - Stronger stock markets helped stabilise crude oil prices on Wednesday yet concerns about oversupply persisted.
Asian shares extended global stock market gains, with markets in China stabilising and Japanese stocks posting their biggest one-day gain since the height of the global financial crisis in 2008.
The pan-European FTSEurofirst 300 index .FTEU3 was up more than 2 percent in early trade. MKTS/GLOB ID:nL4N11F01S
Traders said the upbeat sentiment had flowed into oil.
"Fundamentally, the market is following the stock market," said Tamas Varga of PVM. "That's why the oil market is pretty stable."
Brent crude LCOc1 was trading at $49.61 per barrel at 0908 GMT, up 9 cents from the previous evening's close, after jumping 4 percent in the last session.
U.S. West Texas Intermediate crude CLc1 was down 6 cents to $45.88 after falling in the previous session as the end of the U.S. summer driving season pointed to lower fuel consumption.
Yet concerns remained that high global oil production is butting up against weakening demand growth, especially as growth in China slows.
"The oil market is still oversupplied," Varga added. "The strength is going to be temporary."
Oil prices have fallen by more than 50 percent since June 2014 as a result of a global supply glut.
Prices have seesawed in recent weeks on concerns about Chinese growth and a slide in its equity markets.
The Organization of the Petroleum Exporting Countries (OPEC) is also producing close to record volumes to squeeze out competition, especially from U.S. shale producers.
There was also news that Russia and Mexico would not cut production, cooling speculation that some producers might lower output to support prices. ID:nL1N11E1DU ID:nL4N11D0R1
On Wednesday, Britain's oil and gas industry association also said the country's output in 2015 would rise for the first time in 15 years reflecting investment in more efficient technology. ID:nL5N11E2RT