The British government tried to fight back on Sunday against criticisms that it is divided and unprepared for Brexit, saying it will set out detailed plans for the U.K.’s exit from the European Union and issuing a joint statement by two Cabinet rivals over Europe.

Trade Secretary Liam Fox, a strong supporter of leaving the European Union, and the more pro-EU Treasury chief Philip Hammond, wrote in the Sunday Telegraph that they agreed there should be a “time-limited” transition period after Britain formally leaves the bloc in 2019, to avoid a “cliff-edge” for people and businesses.

Mr. Fox and Mr. Hammond said the transition period “cannot be indefinite; it cannot be a back door to staying in the EU.” They didn’t say how long the transition would last or what rules would apply during that period.

The government also said Sunday it wants to increase pressure on the 27 other EU nations to start negotiating a “deep and special” future relationship that would include a free trade deal between Britain and the EU.

The EU says those negotiations can’t start until sufficient progress has been made on three initial issues- how much money the U.K. will have to pay to settle its outstanding commitments to the bloc; whether security checks and customs duties will be instituted on the Irish border; and the status of 3 million EU nationals living in Britain.

The government’s Brexit department said Britain wants to show that progress on the preliminary issues has been made and “we are ready to broaden out the negotiations” by the time of an EU summit in October.

Brexit Secretary David Davis said that “with time of the essence, we need to get on with negotiating the bigger issues around our future partnership to ensure we get a deal that delivers a strong U.K. and a strong EU.”

The push comes after EU officials expressed impatience with the pace of Britain’s preparations.

The bloc’s chief negotiator, Michel Barnier, said last month there was “a clock ticking” on the talks. Irish Prime Minister Leo Varadkar said last week that Brexit advocates “already had 14 months” to issue detailed proposals, but had not.

Mr. Barnier is due to meet Mr. Davis for a new round of negotiations at the end of August.

Britain voted to leave the EU in June 2016, but did not trigger the formal two-year exit process until March.

Prime Minister Theresa May then called a snap election in an attempt to increase her Conservative Party’s majority in Parliament and strengthen her negotiating hand. But voters did not rally to her call, leaving May atop a weakened minority government.

In recent weeks, with Ms. May on her summer vacation, members of her Cabinet have openly disagreed about what direction Brexit should take.

Opponents of Brexit have become increasingly vocal, arguing that the public or Parliament must get the chance to vote on any final deal between Britain and the EU.

David Miliband, who was foreign minister in Britain’s previous Labour government, said leaving the EU was “an unparalleled act of economic self-harm.”

Writing in The Observer newspaper, Mr. Miliband said there must be “a straight vote between EU membership and the negotiated alternative.”