The Conservative Party is being "manipulated" by Brexit "zealots" and the "mainstream majority" of MPs must reassert itself to stop a damaging EU exit, Sir John Major is to argue.
In a lecture in Glasgow, the former prime minister will urge Parliament to "dig deep into its soul" and act before the scheduled departure, on 29 March.
Brexit will cost billions and risk the break-up of the UK, he will say.
Theresa May is continuing talks with the EU to try to salvage her deal.
Parliament rejected the terms of withdrawal negotiated with the EU by a huge margin last month, raising the prospect of the UK leaving without a formal agreement.
Mrs May intends to put the deal to the vote again - although it is unclear when this will happen.
'Wisdom and will'
Speaking at the University of Glasgow, Sir John will say he hopes Parliament has the "wisdom and the will to exert its democratic right" to stop a no-deal Brexit in its tracks and give the people another say on whether to leave.
Sir John, who led the country between 1990 and 1997, will urge MPs to act in the UK's economic interest given what he says is the calamitous threat to jobs, investment and the public services from leaving.
"The decision Parliament takes next week can undermine or revive the reputation of representative politics and from that flows so much of our whole way of life," he will say.
"Every so often, in our long history, there has come a moment when Parliament has had to dig deep into its soul. Now is such a moment."
"I believe we have a right to expect members of Parliament to vote for an outcome that best protects the future welfare and prosperity of our nation - without fear or favour and without deference to party allegiance."
Sir John will suggest "fringe opinion" is driving Conservative and Labour policies towards Brexit, attacking "rogues and chancers" in both parties for whom the "truth is nothing more than a plaything".
The "intransigence" of the European Research Group of Conservative MPs is determining policy, with little regard to the "pragmatic and tolerant" brand of Conservatism that attracted him to the party in the 1960s, he will say.
"Some, who can fairly be called zealots, seem incapable of looking beyond the one issue of Europe," he will say. "It is not just that it dominates their thinking, it seems to obsess them."
While expressing admiration for the seven ex-Labour MPs who quit the party on Monday, he will say a "moderate" Labour party is essential if the centre of British politics is not to be overwhelmed by populism.
"When I refer to the centre, I don't mean some amorphous party of moderates and centrists," he will say.
"When I speak of the centre, I mean that our three main national parties - Conservative, Labour and Liberal Democrat - must each retain a mainstream majority of their own.
"Currently, both the Conservative and Labour parties are being manipulated by fringe opinion.
"Complacent voices dismiss the chances of fringe opinion gaining control of the political agenda.
"Britain is too pragmatic, they say, too stable and our political system too mature. I hope they are right".
The ERG has dismissed Sir John's earlier warnings as sour grapes, accusing him of wanting to overturn the 2016 Brexit referendum vote and ignoring MPs' decision to trigger the two-year process of leaving, in 2017.