You might have to pay to visit the EU post-Brexit
Asked about possible restrictions on British people looking to come into the UK, Rudd told the BBC's Andrew Marr Show on Sunday: "We do not rule it out."
The EU has been considering tighter border restrictions for non-member countries since 2011 and it has become a high priority following the wave of terrorist attacks in France, Germany, and Belgium this year.
Schengen members, of which Britain is not one, will still be free to move throughout the EU. But the new rules under consideration are thought to require non-EU members to apply for visas so they can be vetted.
Rudd said it was possible that Brussels could introduce a system requiring Brits to apply online and pay for a visa before coming to visit an EU country, a bit like travel to the US, once Britain officially leaves. While Rudd did not say whether she thinks this is likely, she did say: "It is a reminder that this is a two-way negotiation."
The Guardian reports that France and Germany favour a system that would require people to apply for a visa at least 72 hours before travelling, at a proposed cost of £10 ($13.20).
Rudd also reaffirmed the government's commitment to reduce net migration to the UK to tens of thousands and finally hinted at some details of how that might actually happen.
She rejected an Australian-style points system but suggested that the UK could introduce a work permit system for EU migrants, saying: "Whether we look at a work permit system or another system is something that my department is looking at closely at the moment."
Labour leadership contender Owen Smith also appeared on the Andrew Marr Show, saying that if he gained power in 2020 and the UK was in recession due to Brexit he would reapply to join the EU.