May is battling to get the Brexit deal she negotiated with the European Union through parliament in a vote scheduled for Tuesday with the treaty facing heavy opposition from lawmakers both for and against Britain leaving the bloc.
"It looks very difficult from where we are trading now as there are multiple scenarios ahead if she fails to win the vote," said Fritz Louw, a currency strategist at MUFG in London.
Sterling was broadly flat at $1.2732 and just shy of a June 2017 low of $1.2659 hit earlier this week. Against the euro and the yen, the pound was flat at 88.98 pence and 143.72 yen respectively.
The proportion of investors looking to raise their holdings of UK assets fell to 15 percent from 21 percent in the third quarter, according to a State Street Survey, indicating investors are growing wary as Brexit talks approach a crunch point.
The pound and the British stock market top the list of bearish bets among global investors due to Brexit concerns though that could lead to a big snap back if an orderly Brexit or no-Brexit are the outcome.
Currency derivative markets painted a picture of relative calm on Thursday as investors remained broadly cautious.