LONDON - Sterling rose to its highest in two months on Monday, as the prospect of steep rate cuts next year by the Federal Reserve dented the dollar, but the pound fell to its lowest since early May against the euro.

The pound got a modest lift from a rise in gilt yields , after Prime Minister Rishi Sunak said his government would turn to cutting tax after a fall in inflation, speaking ahead of this week's budget update when finance minister Jeremy Hunt is expected to announce how he will speed up the stagnant economy.

The pound was up 0.1% on the day at $1.2475, having risen earlier by as much as 0.39% to a session peak of $1.2511, its highest since Sept 13.

The euro was up 0.1% against sterling at 87.61 pence, narrowly below the day's high at 87.70, its strongest since early May.

Hunt said over the weekend he would not deliver tax cuts that might fuel inflation. Official forecasts due on Wednesday are expected to show he has more room for giveaways before running into trouble with fiscal rules than in his annual budget published in March.

"Speculation over tax cuts has centred on inheritance tax and perhaps even income tax and national insurance, which would favour workers at the lower end of the income spectrum. Our UK economist does not, however, think this moves the needle for the Bank of England rate story, where we think rates have peaked and the BoE will start easing next August," ING strategist Chris Turner said.

"Speculation over tax cuts in a risk-positive environment should be good news for sterling. GBP/USD can push up to $1.2590, while EUR/GBP can correct back to 87.00 this week," he said.

Yields on benchmark 10-year gilts were up 5 basis points on the day at 4.153%, underperforming both U.S. Treasuries, which rose 4 bps to 4.478% and German Bunds, which were up 3.8 bps at 2.627%.

Money markets show traders believe the Bank of England will cut rates by about 80 basis points over the course of 2024. Just a week ago, 60 bps were priced in.

(Reporting by Amanda Cooper; Editing by William Maclean)