LONDON, Jan 18 (Reuters) - The British pound edged up on Thursday, extending the previous day's gains after the annual rate of consumer price inflation unexpectedly increased last month, pushing markets to temper rate cut expectations.

The consumer price index unexpectedly increased to 4.0% year-on-year in December from November's more-than-two-year low of 3.9%, giving a lift to sterling and sending bond yields higher as markets wager that the Bank of England (BoE) will keep interest rates higher for longer.

The central bank raised rates 14 times between the end of 2021 and August last year, taking rates to their current 15-year high of 5.25% as inflation rose to a more than four-decade high of 11.1% in late 2022.

Core inflation, which strips out more volatile food, energy, alcohol and tobacco components, stayed at 5.1% in December, in contrast with expectations for a moderation to 4.9%.

"Sterling has fought back on the basis that December's CPI print proved to be stickier than expected," said Kyle Chapman, FX markets analyst at Ballinger & Co.

At 1030 GMT, the pound was up 0.1% against the dollar to $1.2683, extending Wednesday's 0.3% rise that snapped a three-day decline against the greenback.

The pound was down slightly at 85.89 pence per euro , after a 0.2% rise the day before.

Markets quickly moved to price out British rate cuts following the inflation report, with interest rate futures implying a less than 50% chance that the BoE loosens policy at its May 9 meeting, from around an 80% chance late on Tuesday.

Most major central banks are expected to cut interest rates this year, with the Fed still seen as more likely than not to reduce borrowing costs in March and the ECB likely making a move in April.

"In the U.S. and the euro zone you can see that inflation is coming down, but it's certainly less visible in Britain," said Niels Christensen, chief analyst at Nordea.

"The bottom line is that it's a difficult spot for the Bank of England and they will have to wait a little longer for data before seeing whether they can cut in June as the market expects."

(Reporting by Samuel Indyk; Editing by Alex Richardson)