In a warning to clients, the US bank raised fears about the economic impact of Brexit negotiations between the UK and EU breaking down.
The predicted sell-off could result in sterling’s value against the dollar plunging to lows not seen since the mid-1980s.
Kamal Sharma, the bank’s currency strategist, warned that this could spark a “protracted current account crisis” in Britain.
Central banks and sovereign funds currently hold £388bn ($500bn) of UK debt, according to the Daily Telegraph.
The sterling weighting of their reserves is 4.7 percent, significantly above 3.6 percent average over the last 20 years.
A no-deal scenario could have a major impact on this allocation.
David Owen, chief European economist at Jefferies International, said sterling could break below $1.10 against the dollar.
He said: “If central banks start to question the role of sterling as a reserve currency there will be serious consequences. We could see pound dropping to $1.05.”
Neither Jefferies nor the Bank of America believes a no-deal outcome is likely, despite the tensions between UK and EU negotiators.
Other experts warned that the euro faces the prospect of being sold off, sparking major “disruption” for the European Union.
Stephen Jen, a currency expert at Eurizon SLJ, said: “Central banks still have very little trust in the long-term prospects for the euro.
“Brussels needs to think very carefully about trying to punish the UK. It is effectively using the threat of trade sanctions as a weapon.
“But the extreme disruption for the EU itself if this happens would be greater than some might think.
“If you stand back and look at Britain’s ‘CV’, it is actually not bad at all. It has a trusted legal system, a global financial centre, and a lot of soft power.
“The Bank of England is one of the very few central banks on a normalisation path.
“The problems over Brexit will be resolved over time because there is no way that large economies are going to shut their doors to each other and stop talking.
“I think that the UK economy is doing better than people say, and sterling is very cheap at this level.”