Campaigners will write to the government tomorrow saying they are taking it to the High Court in an effort to keep Britain in the single market.
The claimants will seek a judicial review in an attempt to give Britain's MPs a new power of veto over the terms on which Britain leaves the EU, 'The Sunday Times' reports.
The two claimants are Peter Wilding, the chairman of pressure group British Influence credited with coining the term Brexit and remain voter; and Adrian Yalland, a Conservative lobbyist who voted to leave.
The new case follows the same legal path being used in the case that concluded its hearing in the Supreme Court last week.
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If they are successful, Parliament would be able to stop May from meeting her plan to trigger Article 50 and begin formal negotiations for Britain's exit from the economic bloc at the end of March 2017.
But, if the claimants win the new court case, the government would have to gain the approval of MPs over this aspect of exit talks.
The move comes as around 40 rebel MPs from May's own Conservative party, dubbed the "new bastards", prepared to set up a campaign group to fight for a soft Brexit inside the single market.
The High Court has already ruled Downing Street cannot trigger Article 50 of the Lisbon Treaty - the mechanism which fires the starting gun on Brexit talks - without parliamentary approval, a ruling now being examined by the Supreme Court with a ruling expected in January 2017.
The UK voted to leave the EU in a referendum on June 23 by a margin of 51.9 per cent to 48.1 per cent.