However, Downing Street has been privately lobbying EU countries to take a “more pragmatic approach” to the fingerprint tests when they are eventually introduced.

Nick Thomas-Symonds, the minister responsible for negotiating with the bloc, is understood to have raised the matter personally in talks with EU officials.

It raises the prospect that Brussels could demand concessions from Britain in return for any deal, such as the UK accepting a young mobility agreement. EU officials have ruled out that quid pro quo at this stage.

Before the election, Sir Keir said he would persuade the EU to look again at the introduction of fingerprint checks for millions of UK holidaymakers.

But one EU diplomat poured cold water on the idea of a speedy deal, saying that negotiating one would “not be a priority” for the bloc.

It came as Spain decided to impose surprise border checks with Gibraltar.

Madrid warned it would abide by the new EU electronic border rules which make it impossible to continue waiving passport checks and make the hard border permanent, unless a deal was done.

“Spain is ready for the Entry-Exit System to come into force on the date set by the European Commission, which is responsible for that decision and which the Spanish government and the interior ministry will abide by,” a spokesman for the interior minister told The Telegraph.

Madrid has piled pressure on Britain over Gibraltar since Sir Keir Starmer last week surrendered sovereignty of the Chagos Islands but the Prime Minister insists the Rock, ceded to Britain in 1715 after being captured from the French in 1704, will stay British.

An estimated 15,000 Spanish workers cross the border to the Rock every day, while many Gibraltarians have second properties in Spain or travel to the neighbouring region of La Linea to go shopping.