The pound plunged to as low as $1.1983 in early trade in Asia, depths not seen since a bout of thin liquidity triggered a "flash crash" on Oct. 7 that wiped as much as 10 percent off the pound in a matter of minutes.
By 0851 GMT sterling had managed to inch back above $1.20 but still traded down 1.1 percent on the day at $1.2040.
Dealers said the market was reacting to various media reports over the weekend, including one in The Sunday Times that said May will signal plans for a "hard" Brexit in her speech on Tuesday, saying she's willing to quit the European Union's single market to regain control of Britain's borders.
Investors have been worried such a decisive break from the single market would hurt British exports and drive foreign investment out of the country.
"Consistently we've had environments where sterling tends to weaken quite aggressively when May comes in with heavier rhetoric than expected, and this is definitely heavier rhetoric than expected," said Citi's head of European G10 currency strategy in London, Richard Cochinos.
"Broadly, the market has not has sterling and Brexit and Theresa May in its mind for the last two months - it's been driven by Trump and Treasuries, and more the U.S. drivers. And now for two weeks in a row we've had news on May ... really bring that to the forefront again."
Cochinos said Britain's hefty current account and budget deficits meant it was heavily dependent on foreign capital, and that the more uncertainty investors felt over Britain's place in Europe, the more that investment would dry up.
May has said she will trigger Article 50 - starting the formal withdrawal from the EU - by the end of March. But so far, she has revealed few details about what kind of deal she will seek, frustrating some investors, businesses and lawmakers.