LONDON, Oct 2 (Reuters) - British manufacturing activity slowed sharply in September, though less steeply than the month before when it shrank at the fastest rate in more than three years, a survey showed on Monday.

The S&P Global/CIPS manufacturing Purchasing Managers' Index (PMI) remained well below the 50 level dividing growth from contraction, edging up to 44.3 in September from August's reading of 43.0, which was the lowest since May 2020.

September's figure was a fraction higher than an initial "flash" estimate of 44.2.

"The end of the third quarter saw the downturn at UK manufacturers continue. Output, new orders and employment were all cut back further, amid weaker intakes of new work from both domestic and overseas clients," S&P Global said.

The most recent official data showed British manufacturing output fell 0.8% in July although volumes were 3.0% higher than a year earlier.

S&P said 55% of manufacturers expected growth over the next 12 months, fewer than in August, while 9% expected a contraction.

"Optimism was linked to a hoped-for market recovery, planned growth initiatives and a more stable inflationary environment," S&P said.

The fall in overseas demand was broad, spanning customers in mainland Europe, the United States, China and Brazil, reflecting a subdued global economy.

Manufacturers raised prices for the first time in four months as they sought to rebuild squeezed profit margins, although the increase was small. Input costs fell sharply, especially for metal and energy.

The Bank of England is keeping a close eye on factors affecting inflation, including factory-gate prices and companies' profit margins, as consumer price inflation of 6.7% is more than triple the BoE's 2% target. (Reporting by David Milliken; Editing by Hugh Lawson)