Sterling fell to $1.27.80 in early trading today (4 October), its lowest level against the US dollar since 1985. This level is almost 15% weaker than before the EU referendum on 23 June.
The pound has also ploughed to a new three-year low against the euro, at 87.51p.
On Sunday, May said she would trigger Article 50 by the end of March 2017, which means the UK will leave the European Union by the summer of 2019.
Investors are concerned that Britain appears to be on track to leave the EU single market, as it places a priority on restricting immigration into the UK.
Director of research at Forex.com and City Index Kathleen Brooks said: "The Tory party conference is turning into a sell for the pound, as foreign exchange traders get spooked by May's apparent sanguine attitude to leaving the single market, preferring to focus on immigration and UK sovereignty rather than the economic fallout of Brexit."
The falls today take sterling below its previous post-Brexit-vote lows, with the UK's currency also down against 29 of its 31 major peers.
Spreadex financial analyst Connor Campbell said: "The pound's perilous position has continued this Tuesday, with sterling still suffering from the aftershock of Theresa May's hard Brexit promises."