With British Prime Minister Theresa May facing deadlock in parliament over her deal to leave the European Union and the bloc offering little so far, calls for a second referendum are growing louder.

It is not clear what impact, if any, a second vote would have on sterling. Some analysts suggest the currency could jump because it could reduce the risk of a no-deal Brexit but others say it would only deepen the economic and political uncertainty.

Traders appear to be shying away from taking big bets on the British currency with so much doubt about the chances of securing a deal with the EU less than four months before Britain is due to leave the bloc, on March 29.

"The short-term risk premium is still not particularly high suggesting more downside risks for the currency as the March deadline approaches," said Chris Turner, head of foreign exchange strategy at ING.

The pound was flat against the dollar at $1.2599 on Monday, not far off a 20-month low of $1.2477 touched last Wednesday, a day after a planned vote in parliament on May's Brexit deal that was postponed due to expectations that it would be rejected.

Against the euro, the pound fell 0.1 percent to 0.90 pence .

Sterling has fallen for five consecutive weeks against the dollar.

Traders say the 20-month low of below $1.25 hit on Wednesday would act as a temporary support for the battered currency unless there were further clarity on the outcome.

Despite the tough task that May faces in winning concessions from the EU over the Brexit deal agreed on Nov. 25, most investors think the British parliament will eventually back a "softer Brexit" rather than a complete separation from the EU.

May will state her opposition to a second Brexit referendum in a speech to parliament on Monday, telling parliament such a vote would do "irreparable damage" to politics.