Britain’s Brexit Secretary Dominic Raab has said that the UK would not flinch in an impasse with the European Union, after the British Prime Minister’s plans for leaving the bloc were rejected last week.

He was speaking after Theresa May’s first cabinet meeting since her Brexit proposals were rejected in Salzburg.

Speaking to the BBC, he said that Mrs May's cabinet had a "healthy discussion" at the meeting.

"The prime minister made clear we're going to keep our calm, hold our nerve and press the EU on some of the criticisms that they've made, but also to be clear that there are no credible alternatives that the EU has come up with," he said.

Mrs May is under pressure to abandon her proposals by some in her own cabinet who felt the plan kept the UK too closely aligned to the EU.

Ministers who were already unhappy with the Chequers proposals were expected to use the EU's response to put further pressure on Mrs May to change course and seek a simpler, less ambitious deal.

Mrs May has indicated that she has no intention of deviating from her proposals, raising the possibility of further Cabinet resignations ahead of the Conservative party conference next week.

Theresa May insists the Chequers plan is the only credible option on the table

Earlier, a spokesman for Mrs May said she expects EU leaders to bring forward Brexit proposals "promptly".

The prime minister's spokesman told a Westminster briefing Mrs May had told fellow leaders this, and expected progress by the next EU summit in October, stating: "She was clear of the need to make progress promptly.

"The next staging post in this process is the October council."

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Meanwhile, leading Brexit campaigners have urged Mrs May to change course and pursue a free trade agreement (FTA) with the EU.

The Institute of Economic Affairs (IEA) launched a report which outlined an alternative Brexit plan, and said there was nothing to gain from Brexit in Mrs May's current proposal.

The IEA blueprint was endorsed by top Conservative Brexiteers, who insisted a comprehensive FTA was deliverable in Brussels and in the House of Commons.

"If we continue on the present course, Brexit will be a small damage limitation exercise which will weaken the UK and be largely unnoticed by the rest of the world," IEA co-author Shanker Singham told the launch in London.

He said the prize of a more prosperous future for Britain came only from it having an independent trade and regulation policy.

"Without that, there are no gains from Brexit," he said.

The IEA proposal would see full reciprocal market access, no tariffs in goods including agriculture and maximum mutual recognition of regulatory standards.

The plan was backed by David Davis, who resigned as Britain's Brexit Secretary in July over the Chequers plan and Jacob Rees-Mogg, head of the influential pro-Brexit European Research Group of MPs.

Mr Davis said the negotiations were stuck in a cul-de-sac, needed resetting and an FTA was the way out.

But Mrs May's spokesman ruled out moving towards an FTA, saying it could not prevent a hard border on the island of Ireland - one of the main sticking points in negotiations with Brussels.

"The FTA would only apply to the Great Britain-EU relationship, with Northern Ireland effectively remaining in parts of the single market and customs union," he said.

"The PM has repeatedly set out that we must protect the economic and constitutional integrity of the United Kingdom as a whole."

Separately, in his weekly column for The Daily Telegraph, former UK Foreign Secretary Boris Johnson warned that the Chequers plan would play into the hands of Jeremy Corbyn and the Labour Party if the government continued to pursue the same course in the facing of rising public hostility.

"If we go with the Chequers approach, the public will spot it.

"They will see that the UK has become a vassal state, that we have not taken back control, but lost control.

"They will take their revenge at the polls," he wrote.

"I am afraid that Chequers = surrender; Chequers = a sense of betrayal; Chequers = the return of Ukip; Chequers = Corbyn."

Elsewhere, delegates at Labour's annual conference are to vote on a Brexit motion stating that if the party cannot get a general election, it "must support all options remaining on the table, including campaigning for a public vote".

Yesterday, Mr Corbyn said he would back a second Brexit referendum if it was supported by a conference of his party.

Additional reporting PA and Reuters