In early trading the pound hit $1.2861, more than 15 per cent below the levels seen on referendum day.
Against the euro, sterling fell 1 per cent below Tuesday’s closing figure to €1.1625, its lowest level since 2013.
The slide follows a sharp drop on Tuesday following poor performance figures for the UK’s dominant service sector.
Measures by the Bank of England to help prop up the British economy, which include relaxing funding rules for banks to boost lending by up to £150 billion, failed to buoy the pound.
The pound’s continued descent has been attributed in part to concerns that Brexit may cause a crash in British commercial property values and hurt the wider economy.
Angus Nicholson, a market analyst at IG in Melbourne, Australia, said: “Mark Carney, almost the only British leader who seems to not be resigning at the moment, emphasised the challenges the UK economy will suffer in the post-Brexit world.
“Carney’s speech seems to have initiated the dawning of realisation of the longer-term impact of Brexit for many in the markets.”
Asian stock markets slumped on Wednesday led by a near 3 per cent fall in Tokyo.
The Nikkei 225 fell 2.8 per cent to 15,239.23 and South Korea’s Kospi lost 2.1 per cent to 1,947.49. Hong Kong’s Hang Seng index slid 2 per cent to 20,331.33. Australia’s S&P/ASX 200 was down 1.3 per cent to 5,157.90. Stocks in mainland China, Taiwan and Thailand were also lower.