A flexible approach to immigration controls has been signalled by Brexit Secretary David Davis.
Mr Davis told business leaders that changes to migration rules after withdrawal from the EU would not be allowed to damage the economy.
The Brexit Secretary said that it was in no one's interest to see labour shortages in key industries.
He told CBI Wales in Cardiff: "As we take back control of immigration by ending free movement as it has operated before, let me also say that we won't do so in a way which is contrary to the national economic interest.
"Because, as the Chancellor has said, Britain must win the global battle for talent. No one wants to see labour shortages in key sectors. That won't be in anybody's interest."
The intervention came after staunch Leave campaign Mr Davis provoked anger among Brexit MPs by saying the UK could pay Brussels to obtain the best possible access to the single market after it quits the bloc.
As the row continued, Downing Street moved to play down reports that Prime Minister Theresa May had been snubbed by European Council president Donald Tusk, who failed to invite her to an end-of-year dinner with EU leaders at a Brussels summit.
A government spokesman told the Press Association: "It is well known that Donald Tusk wanted to change the arrangements for the European Council and this timetable reflects those plans, with a one-day meeting instead of two.
"It is no surprise that the 27 other countries will meet after the European Council. Indeed it is recognition that the UK is leaving the EU and that our European partners need to prepare for the negotiations, just as we are, so that we can secure the best outcome for the UK and the EU."