Ms Rudd said reports the European Commission is considering plans for a visa waiver programme to operate across the Schengen free movement area is a “reminder” that the UK is in a “two-way negotiation” with the EU as it seeks its divorce from Brussels.
She agreed that people would be “surprised” if they had to apply for short-term leave to visit countries like France but insisted such a scheme could be rolled out.
Labour warned a family of five could face a £50 charge for a European holiday unless the government fought to keep free movement between Britain and the UK in Brexit negotiations.
Last week it emerged that the French and German governments had suggested modelling a European Commission proposal for a common visa waiver programme on the US Esta scheme.
Visits to America from countries that do not require full visas must apply online for permission to enter the country, at a cost of $14, or £10.
The Home Secretary told the BBC’s Andrew Marr Show: “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 give the best negotiation.”
Ms Rudd said the UK will be able to control its borders post-Brexit but stressed any measures introduced would have to be “reciprocal”.
Andy Burnham, Labour’s shadow home secretary, hit out at the idea of Britons facing a visa system to visit EU countries. He said: “This is yet another example of the drift and confusion as a result of the government’s failure to plan for Brexit. Ministers should not just accept there’s a cost of £50 for the average family to go on holiday.
“The Home Secretary’s words will not have reassured ordinary families about the cost of Brexit. She seems to be sympathetic to an idea that will put a flat £50 tax on the average family holiday in Europe.
“Tory ministers might think nothing of that, but it would make it even harder for ordinary families to afford a holiday. Norway doesn’t have the charge so why should we? I challenge the Home Secretary to rule it out.”