* World stocks dip on uncertainty over U.S. tax reform
* Pound falls on concerns over May's leadership
* European shares fall, but weak pound lifts FTSE
* Stock futures point to lower Wall Street open
* Bitcoin bounces over $1,000
* Graphic: World FX rates in 2017 http://tmsnrt.rs/2egbfVh
LONDON, Nov 13 (Reuters) - Uncertainty over a U.S. tax reform deal pushed world stock markets further away from recent record highs on Monday, while Britain's pound fell on growing concern about the future of Prime Minister Theresa May.
Shares in Frankfurt, Paris and Milan fell around 0.5 percent, but London's blue-chip FTSE held in positive territory as sterling fell by nearly 1 percent, putting it on course for its biggest daily fall in over 10 days.
The overall tone in stock markets was defensive after last week's sudden stumble that began with a slide in Japan. MSCI's world equity index, which tracks shares in 47 countries, was down 0.5 percent -- pulling away from record highs hit last week. It is down for the third straight day for the first time in three months.
Tokyo's benchmark Nikkei fell 1.3 percent, pulling down MSCI's Asia-Pacific Index 0.6 percent. U.S. stock futures pointed to a weak start on Wall Street.
"There have been different explanations for the sell-off in recent days," said David Madden, market analyst at CMC Markets UK. "Stocks don't go up forever but when they do fall everyone says you have to get out."
There was caution as investors waited to see whether a U.S. tax deal would be hammered out soon. U.S. Senate Republicans have unveiled a new plan that differs from the House of Representatives' version and there are few signs of a compromise.
"All eyes are on what the Senate and the House of Representatives will do on their tax bills," said Nobuhiko Kuramochi, chief strategist at Mizuho Securities. "That there is debate is not surprising at all. Still, it is an uphill moment for markets."
The spotlight also fell on the pound, which slipped almost 1 percent to $1.3063 as trouble mounted for May, while Brexit talks face a crucial deadline.
Sterling was set for its biggest one day fall against the dollar since Nov. 2 and was down 0.7 percent at 89.02 pence per euro.
The Sunday Times newspaper said 40 members of parliament from May's Conservative Party had agreed to sign a letter of no-confidence in her -- eight short of the number needed to trigger a party leadership contest.
"The political news over the weekend shows that her (May's) position is coming under increasing pressure and currency markets are reacting to that," said Alvin Tan, a FX strategist at Societe Generale in London.
The dollar was shackled by uncertainty over the fate of the tax cut plans. It fetched 113.32 yen, more than a full yen below its near seven-month high of 114.735 yen touched a week ago.
The euro traded at $1.1651, down slightly after showing its first weekly gain in four weeks last week.
In emerging markets, South African's rand hit a one-year low of 14.54 per dollar, hurt by news that the head of the country's budget office has resigned. The rand has also been hit by concerns about a possible credit ratings downgrade.
Bitcoin bounced almost 12 percent to trade at $6,586 after falling to a 2-1/2 week low on Sunday.
Oil was little changed, trapped between a bullish push from tension in the Middle East and downward pressure from evidence of rising U.S. production, although record fund bets on a rally kept the price in sight of two-year highs.
Brent crude futures were up 3 cents at $63.55 a barrel. U.S. West Texas Intermediate crude gained 10 cents to $56.82.
(Reporting by Dhara Ranasinghe; Additional reporting by Hideyuki Sano in TOKYO and Saikat Chatterjee in LONDON; Editing by Catherine Evans and John Stonestreet)