LONDON, Nov 15 (Reuters) - British annual consumer price inflation (CPI) fell to a lower-than-expected 4.6% in October from 6.7% in September, official data showed on Wednesday.

The increase in consumer prices was the smallest since October 2021.

The Bank of England's staff forecasts and the consensus from a Reuters poll of economists had pointed to a reading of 4.8%.

Annual core inflation fell to 5.7% from 6.1%.

The data represented some rare welcome news for Prime Minister Rishi Sunak who promised to halve price growth this year before an expected 2024 election that opinion polls show his Conservative Party is likely to lose.

But Bank of England Chief Economist Huw Pill said on Tuesday that the expected fall in inflation to just under 5% would still leave it "much too high" even if it represented a more than halving in price growth over the past year.

The BoE has sought to stress that it is nowhere near cutting interest rates from their 15-year high, even as the economy flat-lines close to a recession.

(Reporting by Andy Bruce and David Milliken, editing by William James)