LONDON, Feb 1 (Reuters) - A gauge of British manufacturing growth was its slowest in three months in January as the combined impact of COVID-19 and Brexit weighed on new export orders, and there were signs of disruption of supply chains and mounting inflation pressure too. The final IHS Markit/CIPS manufacturing Purchasing Managers’ Index fell to 54.1, higher than a preliminary reading for January of 52.9 but down from a three-year high of 57.5 in December, when factories rushed to beat problems when Britain’s new trade relationship with the European Union began on Jan. 1. Smaller manufacturers were particularly hard-hit, the survey showed. “Whereas many countries are seeing manufacturers provide a much-needed support to economic growth as the service sector is hit by COVID-19, the UK’s manufacturing sector has come close to stalling,” Rob Dobson, director at IHS Markit, said. Britain’s fast COVID-19 vaccination rollout programme and progress by companies in adapting to Brexit held out the prospect of a pick-up in the pace of growth, he said. “However, there is no swift end in sight to these headwinds, and the longer the current circumstances remain the greater the potential damage to the sector and its suppliers,” Dobson said. Declining new orders and a steep fall in input stocks weighed on the index in January. IHS Markit said supplier lead times jumped because of logistics problems - something which greatly boosted the headline PMI because they are normally a sign of higher demand. Firms said a third coronavirus lockdown, client closures and renewed uncertainty contributed to the fall in output and new orders among small firms. By contrast, medium-sized and large firms saw output and orders rise. Employment levels increased for the first time in a year but only marginally. Input price inflation rose to a four-year high in January, reflecting raw material shortages and transport delays. “Increased costs were passed on to clients, leading to the steepest inflation of selling prices for 28 months,” IHS Markit said. (Reporting by William Schomberg; Editing by Toby Chopra)