The pound slipped against the dollar in Asia trading on Monday as several European countries closed their borders to the UK.
The UK currency fell by 1.2% amid renewed concern about Covid-19 cases in the UK and another EU missed deadline.
The US dollar was buoyed after a $900bn plan to help its economy weather the coronavirus pandemic was agreed on.
Post-Brexit trade talks are set to continue on Monday between negotiators.
The UK and the EU are trying to reach a trade deal before the Brexit transition period ends on 31 December.
The stalled negotiations have been partly responsible for the pound fluctuating over recent weeks, with the currency falling as low as $1.32.
A four-day winning streak pushed it back up to just under $1.36, before it reversed course again.
European nations have begun to impose travel bans on the UK after it reported a more-infectious and “out of control” coronavirus variant over the weekend.
Ireland, Germany, France, Italy, the Netherlands and Belgium are all halting flights.
On Saturday, UK Prime Minister Boris Johnson introduced a new tier four level of restrictions for London and South East England.
“The lockdown news and the stalemate on Brexit is keeping the market nervous,” National Australia Bank’s senior currency strategist Rodrigo Catril told Reuters.