LONDON, Dec 13 (Reuters) - Britain's economy shrank in October, official data showed on Wednesday, testing the Bank of England's resolve to stick to its tough line against signaling cuts to interest rates from their 15-year high.

Gross domestic product (GDP) fell by 0.3% from September, the Office for National Statistics said.

A Reuters poll of economists had pointed to no change in GDP in October.

It was the first time since July that GDP had shrunk on a month-by-month basis.

Sterling fell by about a third of a cent against the U.S. dollar and was weaker against the euro too.

Investors have responded to other signs of a cooling in Britain's economy by bringing forward their bets on when the BoE is likely to cut interest rates for the first time.

However, the central bank is widely expected to keep Bank Rate at 5.25% on Thursday and signal once again that it is not close to cutting them.

Paul Dales, chief UK economist at Capital Economics, said the October GDP reading suggested Britain might be in a recession.

"That may nudge the Bank of England a little closer to cutting interest rates, although when leaving rates at 5.25% tomorrow the Bank will probably push back against the idea of near-term rate cuts," Dales said.

In the three months to October, GDP flat-lined, the ONS said, weaker than the Reuters poll forecast of a 0.1% increase.

Britain's economy avoided a contraction in the July-to-September period - when it also showed no change - but some analysts think it remains at risk of a shallow recession in late 2023 and early 2024 after the BoE's increases in interest rates.

The economy has flat-lined through most of 2023, with the level of economic output now back at its January level.

The ONS data on Wednesday showed Britain's dominant services sector shrank by 0.2% in October while manufacturing and construction contracted by 1.1% and 0.5% respectively.

The economy was 2.0% bigger than immediately before the COVID-19 pandemic hit Britain in early 2020, a stronger performance than thought before recent ONS data revisions but another weak period for living standards nonetheless.

Prime Minister Rishi Sunak and finance minister Jeremy Hunt have promised to speed up economic growth but no significant pickup is expected before a national election that Sunak must call before January 2025.

"October’s negative outturn puts the prime minister’s target to get the economy growing in jeopardy, with high inflation and borrowing costs likely to suppress economic activity in November and December," Suren Thiru, economics director at ICAEW, an accountancy body, said. (Reporting by William Schomberg; Editing by Kate Holton, Andy Bruce and Christina Fincher)