Having edged briefly above $1.26 earlier this morning, sterling fell as low as $1.2524 in late morning trading, 0.5 per cent lower.
It doesn't bode well for May's talks with Trump, which are due to end with a press conference at about six o'clock tonight.
The Prime Minister has vowed to renew the so-called special relationship between the US and the UK, telling a reporter yesterday that "opposites attract". Meanwhile, Trump has apparently referred to May as "my Maggie".
"Today is crucial for the pound," said Paresh Davra, co-founder of RationalFX.
"The Prime Minister’s retort that 'opposites attract', added to the warm welcome yesterday from Philadelphia and Republicans, could set the pound on a stable course.
"The Reagan-Thatcheresque touch to this new geopolitical picture is hard to miss. Positive discussions are highly anticipated and a dialogue over progress and future development could forge true market dynamics.”
May's talks with Trump, the first he has had with a foreign leader, were almost overshadowed by a spat with Mexican President Enrique Pena Nieto, who cancelled a meeting at the White House after Trump mooted a 20 per cent import tax on Mexican goods to pay for his giant border wall.
However, the Mexican peso was having a fiesta today, climbing 0.2 per cent against the dollar to $0.04722. Meanwhile, shares in cement maker Cemex flew as investors fell over themselves to plough cash into any company which might be involved with the wall.
David Cheetham, market analyst at XTB, suggested today's meeting could pave the way for more peaceful negotiations with the Mexican President.
"[Today's] meeting provides an opportunity for Trump to improve his country’s international relations, which have got off to a poor start with the constant aggressive rhetoric surrounding the building of a wall on the southern border causing a Mexican stand-off," he said.
"It seems likely that both will want to have a positive meeting that they can then use as evidence of success to improve their current standings."