British holidaymakers could face a new Brexit charge if they want to visit EU nations once the country leaves the union.
The European Commission set out the plans for a new system of security checks for countries which do not require a visa in a move aimed at preventing terrorists entering the Schengen open-borders area.
Travellers from visa-waiver countries outside the EU will have to pay a five euro (£4.29) fee and complete an online form under the system.
Campaigners seeking to retain close links to the EU warned that the European travel information and authorisation system, called Etias, would represent a new "hidden cost" to Brexit.
The Commission hopes Etias will be up and running in 2020, by which time the UK will have broken away from the EU under the Brexit timetable set out by Theresa May.
Labour MP Stephen Kinnock, a supporter of the Open Britain campaign, said: "Brits travelling to the continent for their holidays will be dismayed at having to pay a fee for something we're used to getting for free.
"Nobody voted for more expensive holidays and an exemption for British travellers to Europe should be something we can negotiate.
"This is yet more evidence of the hidden cost of Brexit."
Liberal Democrat MEP Catherine Bearder said: "This would mean a travel tax and extra paperwork for holidays to Europe, adding to the impact of the falling pound.
"Amber Rudd must clarify how she will ensure British families can continue to enjoy free and easy travel to the EU.
"We must hold this Conservative Brexit government to account and fight to keep Britain open, tolerant and united."
The Prime Minister's official spokeswoman said: "These are proposals that have come forward today and we will need to consider them and study them in detail."
Home Secretary Ms Rudd will discuss the proposals at a meeting with her European counterparts on Friday.
Sir Julian King, the security union commissioner, said: "Terrorists and criminals don't care much for national borders. The only way to defeat them is by working together effectively.
"Etias will help do that: by spotting problem individuals and stopping them from coming, we'll enhance Europe's internal security."
The automated system cross-checks travellers against visa, criminal and stolen document databases.
The European Commission says filling out the form should take less than 10 minutes and the Etias permit will be valid for five years and multiple trips.
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