Former Labour leader Ed Miliband has held talks with pro-EU Tory MPs on trying to force Theresa May to allow a Commons vote on any moves to exit the single market.
A loose cross-party alliance of pro-Europe MPs from all sides of the Commons has expressed concern at the sudden pace towards a "hard Brexit" stance by the Government.
Mr Miliband is considering tabling an urgent Commons question demanding the Prime Minister sets out to parliament exactly what its role will be in the major decisions surrounding Brexit.
The former Labour leader, and ex-Lib Dem head Nick Clegg, have formed common ground with the SNP, the Greens, and some Tories to seek a strong voice for the Commons in the Brexit process.
The grouping believes that while Britain narrowly voted to leave the EU, it did not vote to leave the single market.
Mr Miliband said that parliament must remain sovereign.
"Having claimed that the referendum was about returning sovereignty to Britain, it would be a complete outrage if May were to determine the terms of Brexit without a mandate from parliament.
"There is no mandate for hard Brexit, and I don't believe there is a majority in parliament for it either. Given the importance of these decisions for the UK economy ... it has to be a matter for MPs," he told the Observer.
Mr Clegg said the decisions were too big to be taken by Downing Street alone.
"My great worry is that while there will be a vote on repealing the 1972 European Communities Act, which is about the decision to leave the EU, it will be left to the executive alone to decide the terms of Brexit. That would not be remotely acceptable," he told the newspaper.
The move comes after leaders of the CBI expressed alarm at the apparent direction of Government policy towards a hard Brexit option, which they say could see tariffs imposed on 90% of British exports.
The business chiefs have demanded Mrs May rules out the "worst options" of a hard Brexit, such as not having "passporting" arrangements which allow easy access to European markets for the financial service industry.
Mrs May has said she will open the two-year "divorce" negotiations with Brussels by the end of next March, but has made it clear she does not want a Commons vote on the matter beforehand.
The PM has insisted that immigration controls are a post-Brexit priority, but German chancellor Angela Merkel has insisted such a move would be incompatible with the UK remaining in the single market.