Theresa May was under fresh pressure from within the Cabinet after Boris Johnson warned of a Brexit "meltdown" and called for "guts" in exit talks.
In unguarded comments at a private dinner, the Foreign Secretary said there was a risk Brexit "will not be the one we want" and would keep the UK "locked in orbit" around the EU.
At the gathering of the Conservative Way Forward, a Thatcherite campaign group, he branded the Treasury the "heart of Remain" and claimed negotiations were approaching a "moment of truth".
In comments captured in a recording obtained by BuzzFeed News, he said the Prime Minister was "going to go into a phase where we are much more combative with Brussels".
He added: "You've got to face the fact there may now be a meltdown. OK? I don't want anybody to panic during the meltdown. No panic. Pro bono publico, no bloody panic. It's going to be alright in the end."
Mr Johnson suggested Chancellor Philip Hammond's department was "basically the heart of Remain" and said the UK could end up "in the customs union and to a large extent still in the single market".
The Cabinet minister was speaking to around 20 people dining in a private room after a reception at the Institute of Directors on Wednesday night.
He said: "Unless you make the change, unless you have the guts to go for the independent policy, you're never going to get the economic benefits of Brexit. You'll never get the political benefits of Brexit."
Mr Johnson said fears about the border on the island of Ireland were out of proportion.
"It's so small and there are so few firms that actually use that border regularly, it's just beyond belief that we're allowing the tail to wag the dog in this way," he added.
"We're allowing the whole of our agenda to be dictated by this folly."
Mr Johnson also suggested Donald Trump would "go in bloody hard" and "might get somewhere" in the exit talks if he was in charge.
The US president, meanwhile, has grown tired of Mrs May's "school mistress" tone, his allies have told the Daily Telegraph.
His comments are the latest Brexit headache for the Prime Minister, who is in Canada for the G7 summit.
The Foreign Secretary's deputy, Sir Alan Duncan, raised eyebrows in Westminster when he floated the possibility of a referendum on the exit deal.
Mrs May also met twice with David Davis before flying out to the summit amid reports the Brexit Secretary was considering resigning unless she set a clear time limit on the temporary customs arrangement.
Friends of Mr Johnson said: "This was a private dinner under Chatham House rules so it is sad and very disappointing that it has been covertly recorded and distributed to the media."
Michel Barnier, the EU's chief Brexit negotiator, is expected to hold a press conference in Brussels at around 1pm to discuss the latest round of technical talks on the exit process.
Mrs May secured approval from senior ministers for a "backstop" arrangement that could keep the UK in a customs union with the EU beyond the end of 2020.
But there was no fixed deadline in the document published later, which said only the UK "expects" a final customs solution to be in place by the end of December 2021 at the latest.
The document represents the UK's counter to an EU proposal to keep Northern Ireland alone in the customs union after Brexit, which was rejected outright by Mrs May because it would draw a border down the Irish Sea.
In a letter to Tory MPs, obtained by The Times, the Prime Minister described the UK proposal as "unpalatable but at worst temporary" and "in no way the Government's intended or desired" result.
Under the new backstop proposals, if no agreement on customs has been implemented by the end of 2020, a temporary arrangement would ensure that no "tariffs, quotas, rules of origin (or) customs processes" applied to UK-EU trade.
At the same time the UK would be able to strike free trade agreements with other countries.
Mrs May braced herself for possible defeat in the Commons next week on an amendment which would require her to try to negotiate a permanent customs union with the remaining EU.
The PM has rejected most of the amendments made to the EU (Withdrawal) Bill made by peers, accepting only one in full.
Anti-Brexit campaign group Best for Britain has released an open letter to voters calling on them to join the "national conversation" aimed at resolving the "nightmare of Brexit".
It claims public opinion is shifting on Brexit and published a "roadmap" to a fresh vote with a summer of campaigning planned across 100 constituencies.