Michael Gove has warned there would be long-term damage to democracy if the UK does not leave the EU, but admitted a no-deal Brexit would cause “some turbulence”.
The minister in charge of no-deal preparations also predicted no other countries will follow Britain in exiting, although suggested the EU will look "very different" in the next 10 to 20 years.
Speaking in Manchester on the opening day of the Conservative Party conference, Mr Gove said: "The level of our preparations has accelerated massively since Boris (Johnson) became Prime Minister.
"Now, of course, we can't anticipate every risk, we can't guarantee against some turbulence and that's why we'd much prefer it to secure a deal with the EU before October 31."
Mr Gove said the risk to trust in politicians if the UK does not leave the EU is greater than any from a no-deal Brexit.
He added: "While the difficulties caused by leaving without a deal will pass, the damage to our democracy in not getting Brexit done would endure and resound for much longer.
"Our democracy is precious and depends on people trusting us as politicians."
The Chancellor of the Duchy of Lancaster later responded to a question on whether he believes other countries will leave the EU after Britain does.
He said: "I don't think so. The American baseball coach Yogi Berra said never make predictions, especially about the future.
"I think that there are particular reasons why Britain is right to leave the European Union at this time, and I respect the right of other nations to forge their own future.
"So my own hunch is Britain will leave, other countries will stay - but 10, 15, 20 years on, I think we may see a very different European Union to the one we have now."
Brexit Secretary Stephen Barclay, in his speech to members at the conference, said that “delaying Brexit has come at a cost”, adding: “It has cost us trust in our democracy.
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"For those who in good faith at the last general election believed the promises of MPs who said they would honour our vote to leave the EU.
"And it has a massive financial cost - in extra payments to the EU. It costs an extra £1 billion in payments to Brussels every month we delay.
“And how much has the delay cost us in lost opportunities? The very opportunities which we voted for - to lower living costs by forging new trade deals around the world."
Commons Leader Jacob Rees-Mogg highlighted the importance of the DUP's support to any new deal.
He said: "I think if the DUP is happy with the deal, there'll be very few Conservatives - including those who are without the whip - who are then against a deal, and at that point there are a number of people in other parties who think 'yes, we must now just finish this'."
Meanwhile, Foreign Secretary Dominic Raab told the conference that Britain will leave the EU at the end of October “no ifs, no buts”.
He said the government would “strive” for a good deal, but would leave the bloc anyway “if the EU spurns the opportunity for a win-win deal”.
The start of the conference came amid growing pressure on Mr Johnson over a series of political and personal battles, including further questions over his links to US businesswoman Jennifer Arcuri amid reports she told friends they had an affair while he was Mayor of London.
The event also threatens to be overshadowed by moves by Westminster opposition parties to oust the Prime Minister over Brexit.
