The FTSE 100 has opened at a record high, building on last week’s string of positive performances, with sterling weakness providing a Monday boost.
London's blue chip index rose as far as 7,239.26 points, its highest point ever, after ending last week at 7,210.05 points.
Read more: What next for the FTSE 100?
May also suggested that the UK could leave the customs union, which would allow for separate trade deals with other nations.
The Prime Minister said more detail on the government's plans would be available in the coming weeks.
The strong dollar has also weighed on the pound, with cable trading at lows of $1.2165 on Monday morning.
A weaker pound boosts London-listed multinationals by making their foreign earnings more valuable when reported in sterling. The FTSE 100 is heavily weighted towards companies with large earnings in dollars.
Since the Christmas holiday the FTSE 100 has recorded its longest streak of record closes since 1997, ending each successive day with a record close.
Connor Campbell, an analyst at Spreadex, said: “The Prime Minister’s comments were read as falling decidedly on the ‘hard’ end of the Brexit spectrum, with ‘control of [the UK’s] borders’ likely to be prioritised over continued access to the single market.”