The divorce deal, which May agreed last year with the EU, has already been rejected three times by a deeply divided parliament.
The pound sank to $1.275, its lowest level since mid-January.
May's hands have been tied, knowing that to make concessions to Labour would lead to fury in her divided party. Labour has feared any compromises on issues such as workers' rights would be torn up by May's successor.
Britains labyrinthine crisis over Brexit has stunned allies and foes alike, and with deadlock in London, the world's fifth largest economy faces an array of options including an exit with a deal to smooth the transition, a no-deal exit, an election or a second referendum.