Concern over Mr Trump's protectionist policies hit the US currency, helping sterling rise 0.89% to $1.24860, a one-month high.
Meanwhile the benchmark FTSE 100 index shed 47.26 points to 7,151.18.
A stronger pound can hurt multinational firms, as overseas profits are worth less when converted back into sterling.
The biggest faller in the FTSE 100 was bookmaker Paddy Power Betfair. Its shares dropped 4.38% after it said revenues had been affected by a run of "customer friendly" results.
The company said football results in December and Donald Trump's surprise US election win had cost it about Â£40m in the final quarter of 2016.
Electronics giant Dixons Carphone fell by 2.58% ahead of a trading update on Tuesday, however airline Easyjet - which will also update the markets - gained 3.07%.
Miner Antofagasta was the best performing stock, climbing 3.6% and leading other basic resources shares higher. Rival Fresnillo also did well, gaining 3.42%.
Despite its recent gains, the pound is still down by about 17% against the dollar since the Brexit vote in June 2016.
(Close): UK stocks closed lower on Monday as the pound gained against the dollar following Donald Trump's inauguration speech.