Pro-Remain MPs are considering using their Commons majority to keep Britain inside the EU single market if there is a vote for Brexit, the BBC has learned.
The MPs fear a post-Brexit government might negotiate a limited free trade deal with the EU, which they say would damage the UK's economy.
There is a pro-Remain majority in the House of Commons of 454 MPs to 147.
A Vote Leave campaign spokesman said MPs will not be able to "defy the will of the electorate" on key issues.
The single market guarantees the free movement of goods, people, services and capital.
The BBC has learned pro-Remain MPs would use their voting power in the House of Commons to protect what they see as the economic benefits of a single market, which gives the UK access to 500 million consumers.
Staying inside the single market would mean Britain would have to keep its borders open to EU workers and continue paying into EU coffers.
Ministers have told the BBC they expect pro-EU MPs to conduct what one called a "reverse Maastricht" process - a reference to the long parliamentary campaign fought by Tory eurosceptic MPs in the 1990s against legislation deepening EU integration.
Like then as now, the Conservative government has a small working majority of just 17.
They say it would be legitimate for MPs to push for the UK to stay in the single market because the Leave campaign has refused to spell out what trading relationship it wants the UK to have with the EU in the future.
As such, a post-Brexit government could not claim it had a popular mandate for a particular model.
One minister said: "This is not fantasy. This is a huge probability.
"The longer we move away from the referendum, the more the economic pressures will grow to keep some links with the single market."
Another said: "We would accept the mandate of the people to leave the EU.
"But everything after that is negotiable and Parliament would have its say. The terms on which we leave are entirely within my remit as a parliamentarian and that is something for me to take a view on."
Labour frontbenchers say they have also been discussing the option.
One said it would be hard for pro-Brexit MPs to resist the Commons deciding Britain's future relationship with the EU, as it would demonstrate the principle of parliamentary sovereignty eurosceptics have been demanding for years.
One SNP frontbencher said: "Parliament is not going to let Boris Johnson and Michael Gove get away with murder. I just don't think people are going to roll over, particularly on our trading relationship with the EU."
Many pro-Leave campaigners support a limited free trade relationship with the EU, based on the deal about to be signed between Canada and the EU.
It would reduce some barriers to trade in basic goods but other areas - such as services - are largely excluded.
One alternative option put forward by pro-EU MPs would be for the UK to stay part of the single market by continuing its membership of the European Economic Area.
The EEA includes all EU countries, as well as Norway, Liechtenstein and Iceland.
The advantages of EEA membership for non-EU countries - known by some as the "Norway model" - include access to the single market without having to agree agriculture or fishing quotas, to cooperate on justice or foreign affairs, or be a member of the eurozone or the Schengen border-free arrangement.
The disadvantages include having to make a contribution to the EU budget, accepting the free movement of people, and having little ability to influence EU rules.
Stephen Kinnock, the Labour MP for Aberavon, said: "If the British people voted to leave the EU that's one thing.
"But can we really say that they voted for the devastation and destruction of the entire exporting sector of our economy? I don't think you can necessarily say that there's a democratic mandate for that."
But he warned there could be a constitutional crisis if MPs voted to keep Britain's borders open, something people would have rejected in the referendum.
"In a sense it's a lose-lose situation. I don't see how you untie that Gordian knot because you're looking at a massive economic crisis going down the track of the Canada model and a constitutional crisis going down the track of the Norway model."
Pro-EU MPs could use their voting muscle later this year when a post-Brexit Tory government would be expected to put its negotiating plans to parliament.
The government would struggle to negotiate with the EU if it could not secure the support of the Commons.
MPs could also bring pressure to bear once the withdrawal agreement has been settled and a huge amount of legislation would have to be changed.
The European Communities Act 1972 that took Britain into the EU would have to be repealed.
New Acts of Parliament would be needed to implement the withdrawal agreement. Acts that implement EU directives would need to be repealed or amended.
Thousands of EU regulations - that were automatically transferred into UK law - would have to be reintroduced, amended or allowed to lapse. And secondary legislation dependent on the European Communities Act would also have to be given new enabling laws.
Ministers say this process could take years and would provide determined pro-EU MPs lots of opportunity to cause trouble.
Charles Grant, director of the pro-EU Centre for European Reform think tank, said: "I think it is quite possible that Parliament would vote to impose the Norway model on a post-Brexit Tory government.
"Boris Johnson and Michael Gove are free marketers down to their finger tips and might be quite happy to be beaten up by Parliament and have this model imposed on them. They might protest but secretly quite like it. The pressure for Britain to retain some linkage with the single market would be overwhelming."
One senior Tory MP said: "There is all this talk of eurosceptics engaging in guerrilla warfare after a vote for Remain. It could be the other way round.
"The overwhelming majority of Labour, SNP, odds and sods and a hard core of Conservative MPs could make life very difficult."
Another said there would be "enormous pressure" from businesses to get "much better access to the single market".
One Labour MP added: "There will be as much fun and games as possible to stop it and block it and delay it."
Another said the government may try to get Labour to support an early general election being called, by voting to suspend the Fixed Term Parliament Act.
A newly-elected Tory government - potentially with a larger majority - would then have a mandate for its renegotiation plan.
Some pro-Leave campaigners also question how pro-EU parliament really is, suggesting that many MPs are backing Remain simply out of loyalty to David Cameron.
A spokesman for the Leave campaign said: "If you vote Leave, Britain will negotiate a British option which will end the supremacy of EU law and take back control of our borders and our democracy and our economy."
A spokesman for the Remain campaign said: "The Leave campaign can't tell us what would happen if we vote to leave. At every point, they have admitted they 'just don't know'. Leaving Europe would be a leap in the dark that would damage our economy, lead to price rises and job cuts. That's why we will be spending the next two and a half weeks campaigning for every vote to protect Britain's future."