By Dion Rabouin

NEW YORK (Reuters) - Stocks on major world markets fell and benchmark U.S. government bond yields hit all-time lows on Tuesday as worries about Britain's exit from the European Union pushed sterling to a fresh 31-year low, triggering a scramble for the safest and most liquid assets.

Investor confidence was undermined by the Bank of England's warning on the economic risks of "Brexit" and its steps to ensure British banks keep lending, as well as by news of a decline in U.S. factory orders and reports of mixed manufacturing and service sector activity in Asia and Europe.

Bank of England governor Mark Carney said global uncertainty could persist for some time and Chinese Premier Li Keqiang said it could be hard for his country to sustain 6.7 percent growth in the second quarter.

"The consequences of Brexit have put a summer UK interest rate cut squarely on the table, exacerbating negative sentiment toward UK-based assets," said Joe Manimbo, senior market analyst at Western Union Business Solutions in Washington.

Investors bought safe-haven assets as a result, like U.S. government debt and the Japanese yen. Ten-year Treasury yields fell to 1.357 percent <US10YT=RR>, the lowest on record, and the yen <JPY=> rose 0.85 percent against the U.S. dollar, earlier hitting a two-week high of 101.46 yen.

Government bond yields around the globe fell, with Swiss yields <CH50YT=RR> negative all the way out to 50 years and British <GB10YT=RR>, German <DE10YT=RR> and Japanese <JP10YT=RR> 10-year yields at or near their lowest on record.

Worries about Italy's banking sector creating larger problems in the EU also weighed on risk sentiment. Banks have been undercut by a spate of non-performing loans and there is a looming threat that Prime Minister Matteo Renzi will resign if he loses a referendum in October on constitutional reform.

Italy's bank sector index <.FTIT8300> fell 1.8 percent on Tuesday and has fallen 30 percent since the "Brexit" vote on June 23, bringing its losses so far this year to 57 percent.

"The Italian banking system is very shaky and there are noises coming out of Rome that this needs to be dealt with on Italy’s terms and not on the EU’s," said Joe Trevisani, chief market strategist at Worldwide Markets in Woodcliff Lake, New Jersey. "That’s serious business."

Wall Street stocks fell with the Dow Jones industrial average <.DJI> ending down 110.12 points, or 0.61 percent, to 17,839.25, while the S&P 500 <.SPX> lost 14.55 points, or 0.69 percent, to 2,088.4 and the Nasdaq Composite <.IXIC> dropped 39.67 points, or 0.82 percent, to 4,822.90.

MSCI's gauge of global stocks <.MIWD00000PUS>, which tracks markets in 45 countries, dropped 1.1 percent.

European shares <.FTEU3> fell 1.53 percent.

Sterling <GBP=> suffered, falling as much as 2 percent to a low of $1.3001, its lowest since 1985.

The euro <EUR=> fell 0.8 percent against the dollar to $1.1086.

Crude oil dipped below $48 a barrel as concern about a potential slowdown in economic growth that would weigh on demand trumped supply outages in Nigeria and other exporting nations.

Brent crude <LCOc1> was down 4.55 percent at $47.84 a barrel and U.S. crude <CLc1> dropped 5 percent to $46.53 a barrel. [O/R]

(Reporting by Dion Rabouin; Editing by James Dalgleish)