The surge in sterling came as regional equity markets pushed higher following a positive lead from Wall Street, with tech firms tracking an upbeat outlook for Apple, energy firms rising with oil prices and dealers cheered by improving US retail sales.
With a key vote on her agreement due later in the day, May said she had secured "legally binding" guarantees with the EU over the main sticking point of the Irish border question.
The news reinforced hopes the country will have some sort of deal in place once it exits the bloc.
If her plan is still dismissed by MPs, there will be a vote Wednesday on whether to continue to leave without a deal -- considered economically catastrophic by many -- and if that fails to pass then another will take place on extending the March 29 exit deadline.
"From today for three days the market will be closely watching the UK lower house votes over Brexit," Mizuho Securities said in a note.
The main scenario is that the Tuesday vote will be denied, the Wednesday vote will approve avoiding a hard landing, and the Thursday vote will decide the extension until the end of June, it said.
"If the extension is pushed back to December 2019 or later, that would be favoured by the market with possibility of the second referendum that may deny Brexit," it said.
The pound has risen about 1.5 percent against the dollar since late Friday, while it is up around two percent on the euro.