Boris Johnson will set out details of his “final” negotiating offer to the EU on Wednesday in pursuit of a “fair and reasonable” Brexit compromise.
The prime minister will address the Tory conference before submitting new proposals, intended to form the legal text of a new Brexit deal, to Brussels.
Only by leaving the EU on 31 October can the UK “move on”, he will argue.
The public will no longer be “taken for fools” by those who want to delay or block the process, he will claim.
On the eve of his speech, Mr Johnson told a conference fringe meeting in Manchester, hosted by the DUP, that he hoped to reach a deal with the EU over the course of “the next few days”.
The government has insisted it will not negotiate a further delay beyond the Halloween deadline, saying this would be unnecessary and costly for the UK.
However, under the terms of a law passed by Parliament last month, the prime minister faces having to request another extension unless MPs back the terms of withdrawal by 19 October – two days after a summit of European leaders.
On Tuesday, Mr Johnson dismissed leaked reports that customs posts could be set up on either side of the border between Northern Ireland and the Republic of Ireland.
He said suggestions the UK wanted “clearance zones” for goods as part of a package of alternative arrangements to replace the Irish backstop were wide of the mark.
While he conceded some customs checks would be needed as the UK leaves the EU’s customs union and single market, he said technology could keep them to an “absolute minimum”.
The BBC’s Europe editor Katya Adler said the mood in Brussels was “not optimistic”.
She said EU leaders feared the prime minister’s proposed alternative to the Irish backstop could mean the bloc abandoning its red lines – something member states were not willing to do at the moment.
‘Grave consequences’
In his keynote speech to the party faithful in Manchester – his first as prime minister – Mr Johnson will unveil what he hopes will be the basis of a compromise that can win the backing of MPs.
He will suggest that voters are “desperate” for the country to focus on other priorities and will contrast his determination to leave on 31 October with the “years of uncertainty” that he says would result from a Labour government promising another referendum.
“What people want, what Leavers want, what Remainers want, what the whole world wants – is to move on,” he is expected to say.
“I am afraid that after three-and-a-half years people are beginning to feel that they are being taken for fools.
“They are beginning to suspect that there are forces in this country that simply don’t want Brexit delivered at all.
“And if they turn out to be right in that suspicion then I believe there will be grave consequences for trust in democracy.
“Let’s get Brexit done on October 31 so in 2020 our country can move on.”