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The IHS Markit/CIPS manufacturing purchasing managers' index (PMI) dropped to 55.3 in January, its lowest since June 2017, though still well above its long-run average of 51.7.
If sustained, that performance would lead to quarterly growth of 0.6 percent for the sector -- better than the broader economy but only half the rate of the final three months of 2017.
The survey also showed one of the biggest jumps in the cost of raw materials in decades.
Exporters have been helped by last year's global economic recovery, which is expected to carry on in 2018.
While manufacturers reported improved growth in exports during January, the PMI's gauge of total new orders declined, pointing to weaker domestic demand.
Sterling weakened slightly against the dollar after the figures.
"The January PMI fuels suspicion that while the outlook for manufacturing continues to look bright on the export side, domestic conditions could well prove challenging over the coming months," said Howard Archer, economist at the EY ITEM Club consultancy.
January's data showed foreign demand was still growing at one of the fastest rates in the past four years.
But British manufacturers have not done as well as their competitors in continental Europe and the prospects at home for 2018 do not look so bright. Despite improving in January, the British PMI's gauge of factory export orders lagged behind all other major European economies.
Overall new orders expanded at the weakest pace since June 2017.
Consumer goods makers in particular have suffered from weak domestic demand due to higher inflation.
Bank of England Governor Mark Carney said on Tuesday that business investment was lower than it should be due to uncertainty about Britain's future trade relations with the European Union, which it is due to leave in March 2019.
Oil prices rose to their highest in more than three years last month, and Thursday's data showed manufacturers reported their third-biggest monthly increase in costs since the survey started in 1992.
Oil, chemicals, foodstuffs, metals and plastics all became dearer, and factories passed some of the extra cost on to customers.
This may concern the BoE, which is reassessing how fast inflation will fall this year. Inflation peaked at its highest in more than five years in November, when the central bank raised interest rates for the first time in more than a decade.
"The move in the price balances of the manufacturing PMI highlights the risk that consumer price inflation may not slow that quickly, even as the influence of past FX depreciation wanes," Nomura economist George Buckley wrote.
Most economists expect the BoE will not raise rates again until November, though a minority think an increase will come in May. The central bank will set out its latest thoughts on Feb. 8.