Britain's Secretary of State for Departing the EU David Davis arrives for a cabinet meeting in Downing Street, London, January 17, 2017. REUTERS/Neil Hall

LONDON (Reuters) - Britain’s Brexit minister David Davis said the government had received positive responses from Brussels after Prime Minister Theresa May set out her priorities for upcoming negotiations on leaving the European Union.

“Some of the other responses we got back from Brussels overnight reflected that, that this was a positive response, something that they were, I think they were hoping for, frankly,” Davis told BBC radio on Wednesday.

May said in a speech on Tuesday that Britain would seek the greatest possible access to European markets but aim to establish its own free trade deals with countries beyond Europe, and impose limits on immigration from the continent.

Asked how things would change for Britons the day after the country left the EU, Davis said he did not expect travel restrictions but customs checks were up for negotiation.

“You won’t see any difference, let’s say, in the right to travel. We have got 35 million people who come here from Europe each year,” he said. “We will see (about customs checks). That is one of the things we will have to negotiate.”