* Graphic: World FX rates in 2020 tmsnrt.rs/2egbfVh * Graphic: Trade-weighted sterling since Brexit vote tmsnrt.rs/2hwV9Hv (Updates rates, adds chart) LONDON, Jan 22(Reuters) - Sterling fell on Friday as Britain’s third national lockdown sparked the sharpest drop in business activity since May, while data showed retail sales remained weak in December after store closures the previous month. With services companies hit hardest, the preliminary “flash” IHS Markit/CIPS UK Composite Purchasing Managers’ Index fell more than expected to 40.6 in January, well below the 50 threshold that indicates growth and down from 50.4 in December. The weak PMI numbers followed data showing British retailers struggled to recover in December after shops in England emerged from a four-week November lockdown. “The PMI reading itself wasn’t a shock,” said Simon Harvey, senior FX market analyst at Monex Europe. “It highlights what the retail sales data eluded to earlier, that January’s data will be a bitter pill for markets to swallow,” he said. Sterling was 0.5% lower against the dollar at $1.3660 by 1550 GMT, but still on track for a second week of gains against the greenback. Versus the euro, sterling also dropped 0.5% to 89.07 pence, after hitting a 8-month high of 88.30 pence in the previous session. As England is now in its third national lockdown and officials have not confirmed when it will end, the narrative for a quicker economic recovery thanks to the vaccine rollout is fading, knocking down the British currency. “There are already signs that the GBP rally could be running out of steam,” said Jane Foley, head of FX Strategy at Rabobank. She added that weak economic data, coupled with the “suggestion that schools may not open until April, with non-essential shops opening even later in England, bodes poorly for the recovery story”. Britain recorded another 1,290 deaths on Thursday from COVID-19, down from a record 1,820 the day before. IHS Markit said the post-Brexit shift to a more bureaucratic trading arrangement with the European Union had also contributed to the PMI decline. Data released on Friday also showed that public borrowing in Britain for December came in at 34.1 billion pounds, slightly above economists’ forecasts, taking borrowing since the start of the financial year in April to a fresh record high of 270.8 billion pounds.