The pound has dropped to a 31-year low as trading as investors fret over the British government's suggestion it will focus on controlling immigration in its talks to leave the European Union, ahead of retaining close ties to the bloc's single market.

Investors have been selling the currency since a speech on Sunday by Prime Minister Theresa May, who said her government plans to start the process of leaving the European Union by the end of March 2017.

The pound fell another 0.5 percent on Tuesday to $1.2760, its lowest point since 1985.

Kathleen Brooks, research director at Forex.com, and City Index says foreign exchange traders are "spooked by May's apparent sanguine attitude to leaving the single market, preferring to focus on immigration and U.K. sovereignty."

Treasury chief Philip Hammond's comments suggesting turbulence in the coming years compounded concerns.