* Bank shares drive world stocks to 3-month low after Brexit vote

* Wall Street set to follow Europe and Asia lower

* Sterling drops more than 3 percent to fresh 31-year low

* Safe havens in demand; Japan raises yen intervention rhetoric

* Bond yields drop, Spain outperforms after Sunday election

By Nigel Stephenson

LONDON, June 27 (Reuters) - World stocks tumbled and European bank shares were on track for their biggest ever two-day fall on Monday as the political and economic fallout of Britain's shock vote to leave the European Union drove sterling to a fresh 31-year low against the dollar.

Faced with a second day of turmoil after Thursday's referendum, which most in markets had thought would deliver a vote in favour of staying in the EU, investors sought safe havens such as the yen, gold and core government debt.

But moves were not as extreme as on Friday when stocks fell by their most in almost five years.

British finance minister George Osborne sought to reassure markets, saying the world's fifth-largest economy was strong enough to cope with the Brexit-inspired volatility, but the positive impact on sterling was only fleeting.

"This Brexit decision has taken the markets by total surprise. I would remain on the sidelines - no reason to step in yet," said Hampstead Capital hedge fund manager Lex Van Dam.

Markets bet on a further cut in Bank of England interest rates, almost fully pricing in a 25 basis point cut by the end of the year in another blow to sterling and to banks already facing reduced earnings as a result of Britain leaving the EU.

An index of European bank shares fell 7.3 percent, taking losses in the last two trading days to around 20 percent. Royal Bank of Scotland sharese fell 24 percent while Barclays shed 18 percent.

Italian banks also suffered. UniCredit fell 7.4 percent. The government was looking at options to help its banks and prevent further share price falls.

The pan-European FTSEurofirst 300 stocks index , which fell 7 percent on Friday in its biggest plunge in nearly eight years, lost a further 2.5 percent on Monday.

Britain's FTSE 100 index ebbed a further 1.5 percent on Monday and Germany's DAX lost 1.8 percent.

Spain's IBEX index initially rose after acting Prime Minister Mariano Rajoy's People's Party fared better than expected in weekend elections but the gains melted away and the index was last down a modest 0.5 percent.

World stocks measured by MSCI hit their lowest level since March. U.S. index futures were down 0.6 percent, indicating Wall Street would open lower.

Sterling fell 3.7 percent to as weak as $1.3192, surpassing its Friday low as yields on 10-year British government debt fell below 1 percent for the first time.

It fell 2.5 percent to 83.33 pence against the euro and 3.8 percent to 134.12.10 yen .

"Uncertainty equals currency weakness, we know this, and there is no sense that this (sterling) is a value trade right now and that you have to get back in. It is too early for anyone to start calling a bottom," said Neil Mellor, a currency strategist at Bank of New York Mellon in London.

The euro, also considered vulnerable to the exit from the EU of its second-largest economy, fell nearly 1 percent to $1.1016, off a low of $1.0980. The yen strengthened to as high as 101.43 per dollar per dollar .

Government officials stepped up warnings that they could intervene in currency market to stabilise the yen, whose strength harms exporters.

This helped Japan's Nikkei 225 share index, which closed 2.4 percent higher. MSCI's broadest index of Asia-Pacific shares outside Japan fell 0.4 percent. Companies with UK exposure in particular came under pressure.

Yields on core government debt fell again. German 10-year bond yields, the benchmark for euro zone borrowing costs, fell as low as minus 0.1 percent but held above Friday's record low of almost minus 0.17 percent.

Spanish 10-year bonds outperformed those of other lower-rated southern euro zone countries. Their yields were down 17 bps at 1.47 percent after Sunday's election.

U.S. Treasury yields also fell. The 10-year notefell more than 10 bps to as low as 1.46 percent, still above Friday's low of 1.41 percent.

Gold, which saw its biggest rise since 2009 on Friday, stood at $1,329 an ounce, up 1.1 percent on the day.

Brent crude oil was higher in Asian trade on a view that Brexit would have minimal impact on global oil demand. But, by midday in London, it was down 18 cents at $48.23 a barrel.

(Aditional reporting by Hideyuki Sano in Tokyo, Nichola Saminather in Singapore, Patrick Graham and Dhara Ranasinghe in London; Editing by Toby Chopra) ((nigel.stephenson@thomsonreuters.com; +44 20 7542 8682; Reuters Messaging: nigel.stephenson.reuters.com@reuters.net))