* Falling crude output in Venezuela

* U.S. crude stocks down by 3.9 mln barrels -API

* Bankers warn Brexit to cause uncertainty for some time

* COMING UP: U.S. EIA stockpiles data at 1430 GMT

(Changes dateline to LONDON, updates prices, adds quote)

By Julia Payne

LONDON, June 29 (Reuters) - Oil rose on Wednesday as traders poured money back into markets hit by the initial shock of Britain's vote to leave the European Union while a potential oil workers strike in Norway and a crisis in Venezuela also provided support.

Brent crude futures were up 49 cents at $49.07 per barrel at 1017 GMT. U.S. crude was had climbed 57 cents to $48.42 a barrel.

Both benchmarks gained on Tuesday after markets shook off some of the shock from the referendum in Britain.

"Right now, post Brexit, different asset classes are highly correlated and the bounce back in oil price reflects the broader move we seen in equities and FX markets," said Harry Tchilinguirian, global head of commodity strategy at BNP Paribas.

Standard Chartered said that it expected oil prices to return to $50 per barrel rapidly as the Brexit referendum's impact on demand was limited.

Despite that, some bankers said that the knock-on effects from Britain's EU exit vote could continue for some time.

"Uncertainty and volatility ... are both likely to be persistent for a long time to come," Citi analysts said.

On the supply side, a looming strike by Norwegian oil workers threatened to cut output from the biggest North Sea producer.

In crisis-struck Venezuela, oil producers and refiners were struggling to keep output up due to power outages and equipment shortages, traders said.

Additionally, data from the American Petroleum Institute (API) on Tuesday showed that U.S. crude inventories fell by 3.9 million barrels in the week to June 24, far more than the 2.4 million barrels expected by analysts.

The U.S. Energy Information Administration will issue official stockpile data on Wednesday with a fall in crude stocks likely, according to a Reuters poll.

Despite the tightening supply-side, there are concerns that a looming refined products glut, especially in Asia, might spill back into the crude market as refiners cut output. editing by Jason Neely) ((julia.payne@thomsonreuters.com; +44 207 542 1836))