* Graphic: World FX rates in 2020 tmsnrt.rs/2egbfVh * Graphic: Trade-weighted sterling since Brexit vote tmsnrt.rs/2hwV9Hv LONDON, Feb 10 (Reuters) - Sterling edged up against the dollar on Wednesday, breaking above $1.38 and touching its highest level in almost three years as Britain’s speedy coronavirus inoculation programme supports the currency. The pound has gained broadly in the past few weeks amid optimism over Britain’s rapid COVID-19 vaccination roll-out, while its Brexit deal with the European Union has also removed some pressure from the currency. Sterling was up 0.3% to $1.3850 against the dollar as of 0934 GMT, hitting its highest level since April 27, 2018. Versus the euro, sterling traded 0.2% higher at 87.54 pence . “GBP bulls have been flexing their muscles since the start of the year based on relief about the EU/UK trade deal and on hopes that the relatively rapid vaccine roll-out programme will lead to a fairly fast economic recovery this year,” said Jane Foley, head of FX strategy at Rabobank. She pointed out that this week there was a lack of UK economic data to challenge this optimism, but warned that GBP bulls are unlikely to face a smooth ride. “The bumpy relationship between the UK and the EU, issues with the Northern Ireland protocol and border issues suggest that Brexit is still casting a shadow”. In the meantime, the Bank of England’s decision at its latest meeting to give British lenders at least six months to prepare for the possible introduction of negative interest rates has also supported the pound, with money markets pushing forward expectations of a rate cut to March 2022 from August 2021. Britain has moved to tighten travel restrictions from next week and it will require passengers arriving from countries where worrying coronavirus variants are spreading to pay for 10 days of quarantine in hotels. Rule-breakers will face heavy fines or jail terms.