The group, named #StandUp4Brexit, is urging the Prime Minister to scrap the controversial Brexit plan agreed by the Cabinet in July.
Campaign supporters want Mrs May to deliver a clean break from Brussels, as promised in last year's Conservative election manifesto.
They argue that the Chequers plan would keep the UK tied to Brussels and make it difficult for Britain to strike overseas trade deals.
Mrs May's proposal is also hugely controversial because it could force the UK to accept rulings from the European Court of Justice (ECJ).
Ex-party leader Iain Duncan Smith and former ministers Priti Patel and Steve Baker are among the 20 Tory MPs backing #StandUp4Brexit.
Tory activist Rebecca Ryan, who helped set up the grassroots campaign, said it was crucial that Mrs May ditches the Chequers agreement.
She told Express.co.uk: "There was an immediate sense of shock and betrayal when the Chequers deal was announced.
"The Prime Minister U-turned on what she promised in the election manifesto and in her Lancaster House speech in January.
MPs including Iain Duncan Smith have rounded on the Chequers deal (Image: GETTY)
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"Lots of people who have lent their support to the Conservative Party feel angry that they aren't being listened to.
"We believe all of her red lines have been crossed.
"Her plans to agree a