By Dion Rabouin

NEW YORK (Reuters) - U.S. stocks reversed early losses to close higher on Wednesday, but bourses in most parts of the world fell on fears of instability in the European Union and global economic stagnation, while Britain's pound sank below $1.30 for the first time in more than three decades.

Wall Street turned higher, notching modest gains on positive U.S. economic data and a late jump in oil prices.

The Dow Jones industrial average <.DJI> rose 78 points, or 0.44 percent, to 17,918.62, the S&P 500 <.SPX> gained 11.18 points, or 0.54 percent, to 2,099.73 and the Nasdaq Composite <.IXIC> added 36.26 points, or 0.75 percent, to 4,859.16.

Stocks in Europe <.FTEU3>, emerging markets <.MSCIEF> and most of Asia <.MIAPJ0000PUS> all fell more than 1 percent, as global investors shunned risk in favor of safe-haven plays.

MSCI's all-world stock index <.MIWD00000PUS> fell 0.4 percent.

Wall Street got a boost from Institute for Supply Management data showing U.S. service sector activity hit a seven-month high in June as new orders surged and companies hired more workers.

U.S. Treasury yields also edged up late, after 10-year and 30-year yields touched all-time lows. The 10-year yield <US10YT=RR> fell as low as 1.321 percent and the 30-year <US30YT=RR> touched 2.098 percent. [US/]

Minutes from the U.S. Federal Reserve's June policy meeting had little impact. They largely showed U.S. central bank officials concerned ahead of the "Brexit" vote, which subsequently erased $3 trillion from global equities over two days.

Markets look next to Friday's U.S. non-farm payrolls report, analysts said. Last month the Labor Department reported U.S. employers added only 38,000 jobs, far below the 164,000 increase anticipated by economists and the third straight month the jobs report missed expectations.

"The concern is that if we get another bad number after the last one then you could easily see people start (worrying) again about U.S. recession risk," said Luke Bartholomew, an investment manager at Aberdeen Asset Management in London.

Other safe havens gained, with gold <XAU=> touching a more than two-year high and the yen hitting a 3-1/2-year high against the British pound <GBPJPY=>, and to two-week peaks versus the dollar <JPY=> and euro <EURJPY=>.

Henderson Global, Columbia Threadneedle and Canada Life on Wednesday became the latest British commercial property funds to suspend trading, joining three others worth about 10 billion pounds, in the first sign of markets seizing up since Britain's vote to exit the EU.

Money markets are pricing in a good chance of a cut in one or more of the Bank of England's official interest rates to zero within the next three months. Sterling <GBP=D4> fell as low as $1.2798 overnight before recovering to $1.2929.

China, which has been weakening the yuan <CNY=> while eyes are fixed on Europe, allowed its currency to fall to another 5-1/2-year low against the dollar overnight.

The easing has helped China's bourses remain in positive territory with the Shanghai Composite Index <.SSEC> adding 0.4 percent for a fourth straight day of gains and the blue-chip CSI300 index <.CSI300> rising 0.3 percent, its eighth straight rise.

Oil prices rose, settling almost 2 percent higher after a two-day decline lured buyers back. After settlement, oil jumped more, when the American Petroleum Institute reported U.S. crude and refined product stockpiles fell 6.7 million barrels.

Crude futures <LCOc1> jumped 2.5 percent with Brent crude moving to $49.17 a barrel and U.S. crude <CLc1> to $47.81.

(Reporting by Dion Rabouin; Additional reporting by Patrick Graham in London; Editing by James Dalgleish)