Rejoining Erasmus could see the British taxpayers forced to inject some £2 billion into the EU’s budget, according to estimates released by the previous Conservative government.

Lord Frost, who was Britain’s lead Brexit negotiator, said: “Erasmus will always be a net cost to the UK because more EU students want to come to Britain than Brits want to study in Europe.

“That is still the case because we have the best universities and the English language. We don’t need to pay the European Commission to get people to come here.”

His team refused to join Erasmus, unlike research scheme Horizon Europe, because it was deemed a cost burden on taxpayers.

The student exchange programme, which was established in 1987, provides annual grants for students to study around Europe as part of their degree.

While still part of the scheme, Britain was the third most popular study destination, only behind Spain and Germany.

Former prime minister Boris Johnson’s government replaced it with the Turing Scheme, a worldwide exchange programme named after the Bletchley Park code breaker.

European governments insist youth mobility schemes are not tantamount to a back door for immigrants to gain entry to the UK.

“It is not migration, it has nothing to do with migration. It is not freedom of movement through the back door,” German ambassador to the UK Miguel Berger told ITV.

“It simply means that young people between the ages of 18 and 30 can come and work and live and study for [up to four] years, and then they are expected to go back to their countries of origin,” he said.

Negotiations over the EU reset continue as Sir Keir announced a freshly minted trade agreement with Donald Trump.

The deal with Washington will likely cover industries, like steel and aluminium, which were hardest hit by the US President’s 25 per cent import tariffs.

Meanwhile, Brussels has prepared a list of €95 billion of US exports that would face tariffs if it fails to reach its own deal with the Trump administration.

Cars, Boeing aircraft and certain foods, including beef and olive oil were included on the EU’s hit list.