A fortnight in the sun in France or Spain could cost hundreds more and require a visa the Home Secretary has warned, because of a planned crackdown on EU migrants.
Amber Rudd said that she would be “surprised" if other countries introduced visa schemes in retaliation.
But she warned that it could happen as negotiations with other European states would be a “two-way” street.
Today Scottish Tory leader Ruth Davidson will urge her own party to prove to other countries that it wants the UK to be a beacon for liberal and democratic values in the wake of the Brexit vote.
Meanwhile, Labour leadership contender Owen Smith has suggested he would re-apply to join the EU if he became Prime Minister in 2020.
Mr Smith said that he could “potentially” even sign the UK up to the euro.
Theresa May’s government has come under increasing pressure in recent days to define what Brexit will actually mean.
Mrs May has said it must include more controls on immigration.
But last week the Prime Minister dodged questions about whether or not she wanted the UK to stay part of the Single Market.
Today MSPs warn that remaining part of the largest trading market in the world should be a crucial part of talks with 27 other European nations.
Asked about visas, Ms Rudd told the BBC’s Andrew Marr programme: "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."
The Leave campaign’s central message was that the UK could “take back control” including over the UK’s borders if it left the EU.
Ms Rudd said: "Once we leave the EU 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.”
She added that it would be “reciprocal, we are going to have to work out what's in the UK's interests as well going to the EU 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 said that the UK Government was still committed to cutting net migration to the tens of thousands, although she added that that would “take some time".
She backed Mrs May’s rejection of an Australian-style points system, but suggested that work permit system was being considered.
Andy Burnham, the shadow home secretary, said: “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.
"Norway doesn't have the charge so why should we? I challenge the Home Secretary to rule it out."
Meanwhile, Mr Smith said that as well as taking the UK back in to the EU he could also “potentially” sign up to the euro and the Schengen open borders zone.
Negotiations will not begin before next year, meaning the two-year process could end in 2019 just months before the next election, due in May 2020.
In a speech in London to foreign diplomats and journalists Ms Davidson will say that the UK must show it intends to be a "beacon" for liberal, democratic values across the world.
She will say: “We are leaving the EU, we are not leaving Europe, and we will not turn in on ourselves.
"I fought for Britain to stay together in the Scottish referendum two years ago. I did so not just because of the bottom line but because I believe the UK is a force for good.
"Now that we are leaving the EU, more than ever, we must prove to you that we remain that same outward facing nation which wants to play our full part…which seeks to be a beacon for the values we share – of the rule of law, freedom and solidarity with one another.”
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