THE price of post-Brexit border control could be Britons having to apply for visas to travel to continental Europe, the Home Secretary has suggested.

Amber Rudd said reports the European Commission is considering plans for a visa 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 a short-term visa to visit countries like France but insisted such a scheme could be rolled out.

She told the Andrew Marr Show on BBC One: "I think they (British citizens) 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 give the best negotiation."

Control over who comes to the UK was a central issue during the EU referendum campaign.

Ms Rudd said the UK will be able to control its borders post-Brexit but stressed any measures introduced would have to be "reciprocal".

She said: "Once we leave the European Union we will have complete control over who comes into the UK from the EU and who doesn't, with one or two provisos of course.

"First of all, it's going to be reciprocal, we are going to have to work out what's in the UK's interests as well going to the European Union and what works for our economy and making sure that we get the right balance.

"Looking across the whole spectrum is what's going to be the guiding principle."

She also reaffirmed the Tory manifesto commitment to cut immigration to the UK to the tens of thousands.

"I'm completely committed to making sure that we reduce it and yes, tens of thousands, although it will take some time," she said.

Ms Rudd said it is "too early" to outline the specifics of how the Government will achieve its target but she repeated the Prime Minister's rejection of an Australian-style points system.

However, she suggested a work permit system is being considered.

"Whether we look at a work permit system or another system is something that my department is looking at closely at the moment," she said.

She said a work permit system "certainly has value" and "we are not ruling anything out at the moment".

Ms Rudd also addressed her comments from the referendum campaign when she saidBoris Johnson was not the person you want to drive you home at the end of an evening out.

Following the suggestion that Mr Johnson was now driving Brexit in his role as Foreign Secretary, Ms Rudd said: "Boris is not the driver. Theresa May is the driver. The rest of us are in the car."

Ms Rudd also responded to concerns that the number of student visas available to people coming to the UK from non-EU countries could be reduced in order to cut immigration numbers.

She said: "We are looking at a number of options but students do make an important contribution.

"There's going to be no blanket banning of students coming to the UK but we are looking at bringing down the numbers overall."

Andy Burnham, 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."