A trade agreement with the United States will not be enough to make up for the economic damage caused by Brexit, a Cabinet minister said,
US President Donald Trump said he believed a deal could be done "very, very quickly" when he met Prime Minister Theresa May at the G20 summit in Hamburg on Saturday.
But Justice Secretary David Lidington said that while a UK-US deal would be a "very good thing", it would not be "enough on its own" to make up for leaving the EU.
Mr Lidington's comments came as the president of the CBI warned against rushing into "dog eat dog" trade deals and claimed British firms were still in the dark about the business environment they will face after Brexit.
Asked if a US trade deal could make up most of the damage done by leaving EU, Mr Lidington told the BBC's Andrew Marr Show: "It wouldn't be enough on its own, no. But it would be a very good thing to have, as would trade deals with the emerging economies of Asia and Latin America.
"Certainly, one of the frustrations sometimes about being part of the EU is that while the mass of the EU gives it some leverage in international trade, it moves sometimes at a tortoise-like pace because all the member states have to agree a common negotiating position."
The UK on its own would be more flexible and there would be greater opportunities for trade deals, he said.
At the G20 Mrs May said the US, Japan, China and India had shown "great interest in working with us on trade arrangements in the future".
Brexit Secretary David Davis has promised a trade deal with Brussels which would deliver the "exact same benefits" as EU membership, but Mr Lidington said: "That will depend not just on us but on the EU 27."
CBI president Paul Drechsler said businesses were "no wiser" about what the future trading relationship will look like than they were a year ago, and defended the organisation's call for a transitional deal retaining membership of the single market and customs union.
Mr Drechsler told Sky News' Sophy Ridge on Sunday: "As soon as somebody has the plan then of course we can know what the future holds. At the moment we don't."
On the prospect of a US deal he said: "One has to recognise not every trade deal is necessarily a good and fair deal for both parties."
He added: "We are going for headlines rather than the facts and evidence."
Tory Owen Paterson dismissed a suggestion from his Liberal Democrat former cabinet colleague Sir Vince Cable that Brexit might not happen.
Sir Vince, who appears set to be the next Lib Dem leader, told the Andrew Marr Show: "The problems are so enormous, the divisions within the two major parties are so enormous, I can see a scenario in which this doesn't happen."
But Mr Paterson told BBC's Sunday Politics: "I'm afraid Vince is behind history, we are going to leave, we are on target."
He warned: "If we do not deliver a proper Brexit, which means leaving the single market, leaving the customs union and leaving the jurisdiction of the ECJ and taking back control, as we made very clear in the referendum, there will be absolutely appalling damage to the integrity of the whole establishment - not just political, the media and the judicial establishment."
In a sign of the difficulties Mrs May will face in Parliament getting her Brexit legislation through, three Tory former ministers hit out at her approach.
Former attorney general Dominic Grieve and ex-education secretary Nicky Morgan attacked the red line Mrs May has put on allowing any role for the European Court of Justice (ECJ) after Brexit.
Mr Grieve told the Sunday Telegraph the Government should have an open mind on the issue: "We have to be realistic. Some of the attitudes to the ECJ seem to be a bit knee jerk. It has a pariah status.
"I've never been particularly impressed with it, but the fact is it is there and it's going to be doing a lot of work that is relevant to us."
Tory former culture minister Ed Vaizey and senior Labour MP Rachel Reeves used a joint article in the Sunday Telegraph to criticise the decision to pull out of Euratom, the European civil nuclear regulator.
German business leaders also cast doubt on ministers' claims that lobbying by the country's industries will help secure a Brexit trade deal.
Dieter Kempf, president of the BDI, the federation of German industries, told the Observer: "Defending the single market, a key European project, must be the priority for the European Union. Europe must maintain the integrity of the single market and its four freedoms: goods, capital, services, and labour.
"It is the responsibility of the British Government to limit the damage on both sides of the Channel. Over the coming months, it will be extraordinarily difficult to avert negative effects on British businesses in particular."
Ingo Kramer, president of the confederation of German employers' associations (BDA), told the newspaper: "The UK will remain a very important partner for us, but we need a fair deal for both sides respecting this principle. The cohesion of the remaining 27 EU member states has highest priority."
Lib Dem chief whip Alistair Carmichael said: "David Lidington is just saying what everyone knows. That is that the Brexiteers have set off down this route with no plan, and no idea how to make up for all the trade we will lose with Europe with all these mythical trade deals. This would be laughable if it wasn't so important.
"The only person who has shown some interest in talking to them is Donald Trump, but that might change tomorrow based on the president's irrationality.
"The Tories are cocking this all up and putting millions of jobs, investment and our economy at risk."