Shares have also been hit. The FTSE 100 index began the day by falling more than 8%, then regained some ground to stand 2.5% lower.
The more UK-focused FTSE 250 fared even worse, down 8% in early afternoon trading.
Banks were hard hit, with Barclays and RBS falling about 30%, although they later pared losses to below 20%.
The FTSE 100 ended the day 3.15% or 199.41 points lower.
The pound’s dramatic fall started overnight as the outcome of the referendum became clear. At one stage, it hit $1.3236, a fall of more than 10%.
By early afternoon, it had partially recovered, but was still nearly 8% down on the day.
Speaking to BBC Radio 4, Colin Ellis of Moody’s has explained the ratings agency’s decision to downgrade the UK’s credit outlook to “negative”.
He said: “Following the vote there is clearly likely to be a prolonged period of uncertainty now. That will have a negative impact on the UK’s credit standing.
“We don’t know how big that impact will be. It could end up being quite slight if the UK and the rest of the European Union come to a favourable agreement. It could be more pronounced if the negotiations are more protracted or we come to a less favourable understanding.”
The Bank of England said it was “monitoring developments closely” and would take “all necessary steps” to support monetary stability.