By Amanda Cooper

LONDON (Reuters) - Oil fell for a fourth day on Tuesday, swept lower by investor nervousness over next week's vote on Britain's possible European Union exit, which overshadowed signs of a return to health for crude prices.

Safe-haven German Bund yields <DE10YT=RR> fell below zero for the first time while industrial commodities and equity markets, seen as more vulnerable to economic risk, dropped after polls showed Britain's "Leave" campaign leading before a referendum on EU membership..

This overshadowed a more upbeat forecast for oil demand growth from the International Energy Agency, which said the oil market is essentially balanced after two years of surpluses. [IEA/M]

Brent crude oil futures <LCOc1> fell 61 cents to $49.74 a barrel by 1300 GMT, dropping for a fourth day in a row, while U.S. crude futures <CLc1> lost 38 cents to $48.50 a barrel.

"Stock markets are under pressure ... and yields on 10-year German government bonds have slipped into negative territory today for the first time," Commerzbank analysts said in a note.

"Oil prices are unable to ignore this negative market sentiment, especially since the majority of speculative financial investors are continuing to bet on climbing oil prices."

Britain's "Out" campaign has increased its lead over the "In" camp before the June 23 referendum, according to two opinion polls published by ICM on Monday.

"The risk-off mood that has been pervasive in the markets in the last few days has taken hold of oil prices, with weakness in Asian markets and a strong dollar contributing to Brent crude dripping back below $50," said Mihir Kapadia, CEO at Sun Global Investments, which has assets under management totalling $500 million.

If Britain voted to leave the EU, a prospect dubbed "Brexit", investors fear the bloc could slip into recession, which in turn could undermine oil demand.

Reflecting this extreme nervousness, volatility in the pound <GBP1MO> spiked to its highest in at least 20 years, rising even beyond the heights seen when U.S. investment bank Lehman Brothers collapsed in late 2008.

Concerns about Chinese growth are also weighing on sentiment, enough to set aside bullish signs such as a U.S. government forecast on Monday that shale oil output is expected to fall in July for the seventh consecutive month.

OPEC forecast on Monday that the world oil market would be more balanced in the second half of 2016 as outages in Nigeria and Canada help to speed the erosion of a supply glut.

(Additional reporting by Henning Gloystein in SINGAPORE and Aaron Sheldrick in TOKYO; Editing by Dale Hudson and Louise Heavens)