© Reuters. FILE PHOTO: Britain's International Trade Secretary Liam Fox speaks during an interview in Geneva

LONDON (Reuters) - Allowing free movement of people after Britain leaves the European Union would not "keep faith" with the Brexit vote, the international trade secretary said, underlining divisions in the government over the issue.

Liam Fox told the Sunday Times that senior government ministers had not reached a consensus on retaining free movement of people for a transitional period, a proposal outlined by Chancellor Philip Hammond on Friday.

Hammond had said should be no immediate changes to immigration or trading rules when Britain leaves the EU in March 2019, and the status quo could endure until mid-2022.

"If there have been discussions on that, I have not been party to them," Fox told the newspaper.

"I have not been involved in any discussion on that, nor have I signified my agreement to anything like that."

Divisions between ministers over Brexit strategy have become more open after Prime Minister Theresa May lost her majority in an early election she called in June. With May away on holiday, the debate has intensified.

Hammond has led a push within the government to secure a business-friendly Brexit that avoids a sudden change in 2019 in the relationship between Britain and the EU, which buys nearly half the country's exports.

Fox had previously said he backed a transition agreement to smooth Britain's exit from the trading bloc, but on Sunday he indicated that free movement should not continue.

"We made it clear that control of our own borders was one of the elements we wanted in the referendum, and unregulated free movement would seem to me not to keep faith with that decision," he told the Sunday Times.

Fox, who campaigned for Britain to leave the EU in last year's referendum, said any transitional deal needed to be jointly agreed by senior ministers.

"It can't just be made by an individual or any group within the cabinet," he said.

An ally of British foreign minister Boris Johnson also came out against Hammond's plan on Sunday.

Gerard Lyons, a former economic adviser to Johnson when he was London mayor, said a transition period should last for no more than two years.

"Many of the 'risks' being highlighted about Brexit are perceived risks, not real risks. And a two-year transition would alleviate many concerns," Lyons said in a Sunday Telegraph newspaper column.

A growing number of other ministers have said they agree with the need for a transition period but Johnson - who has advocated a tough approach to the Brexit negotiations - has been silent on the issue recently.

Late on Friday, Hammond and Johnson issued a joint statement saying they were "working together to take the UK out of the EU" and its single market, customs union and the jurisdiction of the European Court of Justice. The statement made no mention of transitional arrangements.

(This July 29 story was refiled to fix garble in first paragraph)