Sterling fell below $1.20, its lowest level for more than three months, before bouncing back slightly on Monday morning.
The pound also fell to a two-month low against the euro, trading at around €1.13 on Asian markets.
The drop comes amid reports Prime Minister Theresa May will use a speech on Tuesday to outline her proposal for a so-called hard Brexit.
The term has been used to refer to a deal where curbing immigration is prioritised over access to the single market.
Mrs May has said she rejects the binary definitions of a hard or soft Brexit.
In her speech on Tuesday the Prime Minister is set to outline her plans for Brexit in more detail than ever before, ahead of invoking Article 50, which will trigger Britain's formal exit process from the European Union, in March.
The pound has fallen 20 per cent against the dollar since the European referendum vote in June amid uncertainty about what Brexit will mean for the UK economy.
The latest fall comes as US President-elect Donald Trump told the Times the weakened pound was a “great” thing for Britain as “business is unbelievable in a lot of parts of the UK.”
