Labour, the SNP, Liberal Democrats and other smaller parties revealed they will block a fresh attempt by the embattled Prime Minister to call a general election on Monday in an effort to resolve the impasse.
He accused them of running scared during a visit to Scotland, as the stalemate shows no sign of a breakthrough.
The united opposition, along with former Tory MPs expelled by Mr Johnson, have fast-tracked a Bill through Westminster which would rule out the prospect of a No Deal or force Mr Johnson to seek a three month Brexit extension beyond the scheduled date of October 31.
It was widely held that this left the Prime Minister “boxed in”, but he insisted he will agree to such a move.
“It would mean that the Government of the UK was obliged to write a letter to Brussels asking for a pointless delay to leaving the EU,” he said.
“I don’t think that’s what’s people want and we were very clear about that.
“Not only would it oblige the Government to do that, it would give the EU power to decide how long the UK had to stay in.
“I really, can’t for the life think that that is a democratic way forward. The big picture is we spent a lot of time trying to fudge this thing and I think the British public want us to get out. “They don’t want more dither and delay.”
He insisted a deal would be agreed by 17 or 18 October - the dates of an EU Council summit - and would allow the UK to “start a new partnership with our European friends”.
He added: “We will go to the summit on the 17th, we will get a deal and we will come out on October 31st.”
The cliff-edge constitutional stand-off at Westminster was triggered after cross-party legislation obliging Mr Johnson to seek a Brexit extension cleared the Commons on Friday and will become law after Royal Assent. The House of Lords approved the European Union (Withdrawal) (No. 6) Bill at third reading without a formal vote.
Although it leaves him legally obliged to seek an extension, he is ruling this out.
The legislation requires a delay to Brexit beyond October 31 unless a divorce deal is approved or Parliament agrees to leaving the EU without one by October 19.
It sailed through its final stages in the Lords without amendment and is now expected to receive royal assent on Monday, thereby completing all stages required to become law.
The Prime Minister has previously labelled it the “surrender Bill” and claimed it takes away control of the UK’s negotiations with the EU by allowing Parliament to block no-deal.
Closing the debate in the Lords, Brexit minister Lord Callanan said the Bill brought “delay and uncertainty” while undermining the Government’s efforts to negotiate the Withdrawal Agreement.
He said it also aimed to tie the Prime Minister’s hands when he was seeking to secure the best possible Brexit deal.
But he assured peers the legislation would be presented for royal assent.
“This Bill is about seriously undermining negotiations that could achieve a deal before October 31, frustrating the referendum result and stopping Brexit,” Lord Callanan said.
Earlier, peers rejected by 268 votes to 47, majority 221, a bid to remove an amendment included in the Commons, paving the way for MPs to debate Theresa May’s final Brexit deal during a Brexit extension to next January.
The amendment, tabled by Labour MP Stephen Kinnock, was only passed after tellers for those voting against it were not put forward.
Mr Johnson used his visit to Aberdeenshire to announce that Scottish farmers will receive an extra £51.4 million over the next two years, in addition to the £160 million announced in Wednesday’s spending round.
The PM was expected to stay at the castle before returning to London today to get back to Government businesses.
His girlfriend Carrie Symonds is expected to accompany him on the Balmoral trip.
There were also further signs of unease within the Tory ranks about the uncompromising Brexit stance which saw Mr Johnson boot 21 senior Conservatives - including former chancellors Ken Clarke and Philip Hammond - out of the party in the Commons by removing the whip after they backed the opposition Withdrawal Bill.
Former defence secretary Sir Michael Fallon, who is standing down as Tory MP in Sevenoaks, said he hoped an appeal mechanism would be put in place for his former colleagues.
He added: “I also worry that it sends the wrong message to remainers - particularly in my party.”