London’s benchmark share index was little changed in early trade, despite the sharp fall in the pound.
The FTSE 100 rose initially – to hit a new intra-day high – but then fell back to stand 3.49 points lower at 7,334.32.
The pound fell sharply overnight as traders reacted to reports that Theresa May would use a speech on Tuesday to signal a so-called “hard Brexit”.
Against the dollar, the pound fell below $1.20 at one point, before recovering slightly to $1.2037.
Meanwhile, sterling was down 0.75% against the euro at €1.1376.
In general, the FTSE 100 has benefitted from the weaker pound, as it makes overseas profits for multinational companies listed in London worth more when they are converted back into sterling.
Mining companies were among the biggest risers on Monday, with the Anglo American up 1.8%, but banks were out of favour with both RBS and Barclays down by more than 2%.
The FTSE 100 has been on a remarkable run in the past few weeks, and on Friday closed at its 12th consecutive record high.