The pound surged on Wednesday on hopes that a post-Brexit trade deal between the UK and EU was close.
Sterling climbed more than 1% against the dollar to top $1.35 and 0.75% against the euro to €1.1074.
There were reports that Downing Street sources said a deal could be completed later on Wednesday but that it was “far from certain”.
Shares and sterling were up earlier in the day after France overturned its travel ban for some hauliers.
Lorry drivers trying to get back to France from Dover would have to prove they had a negative Covid test.
But the International Road Transport Union warned that testing stranded truck drivers is “going to be an absolute disaster”.
“The testing is for truck drivers is ridiculous. They are alone in their cabins, they are not spreaders,” warned Raluca Marian, the International Road Transport Union’s general delegate to the EU.
She told the BBC’s Today programme: “We don’t think testing will work. The backlog can’t be cleared if the tests take 30 minutes per driver.”
Ms Marian said that back in spring during the first wave of the coronavirus, temperature checks were introduced at the Austrian Border.
“The tests took around five to 10 minutes but led to 60km of queues,” she said. “But that was a constant flow and we didn’t have the backlog that we have in the UK.”
She called for a testing corridor to be introduced in France to ease the backlog.
The pound had hit a year’s high against the dollar of $1.3581 last week before the borders were closed, but fell back at the start of the week on the news.
Darren Jones, chairman of the Business, Energy and Industrial Strategy Committee, warned delays to the food supply chain because of the lorry backlog will have a knock-on effect on expected Brexit-related delays.
The UK will stop trading under EU rules on 31 December and the government is in talks with the bloc over a Brexit deal.
“There’s an absolute emergency to get those tests through to drivers and get the backlog cleared,” said Mr Jones.
“If the Covid-related backlog is not cleared quickly it will have a cumulative impact on the expected delays around Brexit, even if we are able to secure a deal.
“That will lead to shortages of certain foods on our shelves and disruption to supply.”
Mr Jones said the backlog of lorries was “in many ways was a dress rehearsal for the expected delays on Brexit”.
“The operations were in place, the lorry parks were in place, the systems were supposed to be in place, but they haven’t been stepped up to be ready in time.
This dress rehearsal shows we have a bumpy few weeks ahead.”
The British Retail Consortium also warned there may be shortages of fresh goods until the backlog of lorries waiting to cross the Channel is cleared.
Andrew Opie, the industry group’s director of food and sustainability, said: “It is good news for consumers as the French borders have now reopened, however it is essential that lorries get moving across the border as quickly as possible.
“Until the backlog is cleared and supply chains return to normal, we anticipate issues with the availability of some fresh goods.”