Families were warned of a possible £40 ‘holiday tax’ to travel to the EU as the price of Brexit, after a bombshell Government admission.

Home Secretary Amber Rudd revealed that a Brussels scheme that would require permission to be granted - and a fee paid - before departure could be adopted, saying “We don’t rule it out.”

The scheme is likely to be modelled on the visa waiver system introduced by the United States, which imposes a $14 charge (about £10.50) on every adult and child.

Condemning the ‘holiday tax’, Andy Burnham, Labour’s Shadow Home Secretary said: “Tory ministers might think nothing of that, but it would make it even harder for ordinary families to afford a holiday.”

The warning came after Ms Rudd was asked about a Brussels plan for a US-style visa waiver system and its impact on the UK after it leaves the European Union.

Ms Rudd admitted British people would be “surprised” to learn the free-and-easy travel to the EU they have enjoyed for decades is now in peril.

But speaking to the BBC’s Andrew Marr Show, she said: “It’s a reminder that this is a two-way negotiation.

“The EU and the commissioners may be considering alternatives – they will be considering their negotiations with us, just as we are considering it with them.

“But I am going to make sure that what we do get is in the best interests of the UK.”

Asked about the public’s reaction, the Home Secretary added: “I think they would be surprised. I don’t think it’s particularly desirable, but we don’t rule it out because we have to be allowed a free hand to get the best negotiation.”

The pay-to-visit plan emerged yesterday and is expected to be compulsory for all visitors to the 26-nation Schengen zone – which excludes Britain – from any countries that do not need a visa.

The European Commission is due to reveal draft legislation for the so-called EU Travel Information and Authorisation System (ETIAS) later this year as part of its response to the terror threat.

France and Germany back a system based on the US's Electronic System for Travel Authorisation (ESTA), the Guardian reported.

That requires visitors to the US from countries that do not require full visas to apply online for permission to travel, preferably 72 hours before they leave and pay $14 (£10.50).

Introduced in 2009, in the wake of the 9/11 attacks, US immigration authorities assess whether a visitor is eligible to enter the country under its visa waiver programme, before they arrive at the border.

At present, UK nationals – as citizens of an EU but non-Schengen country – must show a valid passport to enter the zone, but can then travel freely within it.

After Brexit, however, Britons would have to apply through a future ETIAS scheme and pay to visit the continent, legal experts suggested – something Ms Rudd has now confirmed is a real possibility.

Brexit racism and the fightback Show all 9 1 /9 Brexit racism and the fightback Brexit racism and the fightback Demonstrators protest against an increase in post-ref racism at London's March for Europe in July 2016 PA Brexit racism and the fightback These cards were found near a school in Huntingdon, Cambridgeshire, the day after the EU referendum Twitter/@howgilb Brexit racism and the fightback LONDON, UK - JULY 16 : A speaker addresses the EDL members at Hyde Park. About a hundred members of The English Defence League (EDL) march on Park Lane for a rally in Hyde Park. The march on 16 July 2016 was heavily policed keeping the group away from the public. (Photo by David Mbiyu/Corbis via Getty Images) Getty Brexit racism and the fightback Romford, Essex, June 25 @diamondgeezer Brexit racism and the fightback A worker at this Romanian food shop was asleep upstairs at the time of this arson attack in Norwich on July 8, but escaped unharmed. Hundreds later participated in a ‘love bombing’ rally outside the shop to express their opposition to racism and their support of the shop owners. JustGiving/Helen Linehan Brexit racism and the fightback This neo-Nazi sticker was spotted in Glasgow on June 26 Courtesy of Eoin Palmer Brexit racism and the fightback But after news emerged of neo-Nazi stickers appearing in Glasgow, some in the city struck back with slogans of their own. Courtesy of Eoin Palmer Brexit racism and the fightback The Peoples Assembly Against Austerity, Black Live Matters and The Socialist Workers Party organised a march on Saturday July 16th in London, United Kingdom, against austerity, cuts and Racism. The groups also marched in solidarity against Tory government policies. (Photo by Gail Orenstein/NurPhoto via Getty Images) Getty Brexit racism and the fightback More signs began to appear in some parts of the UK, created by people who wanted to show their opposition to post-referendum racism Courtesy of Bernadette Russell

It is thought the only guaranteed way for British citizens to avoid the system would be to accept a Norway-style deal allowing free movement, something Theresa May has rejected.

British residents made more than 30 million holiday trips to EU countries last year, with Spain (13 million visits) and France (8.8 million) the most popular destinations, according to official statistics.

The EU plan is part of a series of measures planned after the Charlie Hebdo and Paris attacks in January and November last year, and the Brussels airport and metro bombings in March this year.

They were viewed as having exposed serious failings in the EU's external and internal border security systems.

In today’s interview, Ms Rudd said she now accepted the target to get net annual immigration down to “the tens of thousands”, having initially cast doubt on it.