The group, almost entirely Tories, set out a series of "red lines" in a letter to the Prime Minister, warning her not to soften Brexit or bend to the will of pro-EU backbench rebels.
The MPs say they "will not accept" any extension of the transition period or the two year Article 50 withdrawal process, remaining part of a customs union "or other similar entity", any exit deal that prevents the UK from forging new trade deals, preferential immigration treatment for EU citizens, Northern Ireland being treated differently to the rest of the EU, or any deal without "robust conditionality", with the £39bn divorce bill withheld until a "satisfactory" free trade agreement is struck.
The letter, which is also signed by one Tory peer and one DUP MP, states: "At this critical moment in our country’s history, the time has now come to get tough in your negotiations with the European Union. We are looking to you to demonstrate courage and leadership in the face of those who seek to undermine the express wish of the British people in the 2016 referendum.
"Our departure must be absolute. We must not remain entangled with the EU’s institutions if this restricts our ability to exercise our sovereignty as an independent nation. Anything less will be a weakening of our democracy. Britain must stand firm."
The letter comes with Mrs May facing a crunch Brexit strategy meeting of the Cabinet at Chequers on Friday amid reports that Ministers such as Chancellor Philip Hammond and Business Secretary Greg Clark, who want close ties with the EU, are winning the argument in Government.
The customs union red line is also potentially significant, with pro-EU Tory rebels gearing up for a parliamentary battle to ensure the UK stays in a version of the trade bloc, which a source said could come before MPs in the last full week of the Commons term, beginning July 16.
A source told The Yorkshire Post the rebel MPs feel they have the numbers to defeat the Government and are unlikely to grant concessions, unlike former Attorney General Dominic Grieve in the recent row over the "meaningful" vote on the exit deal.
Leaver Tory MP Andrea Jenkyns, who recently left her role as a Government aide to speak out on Brexit, was one of the MPs who signed the letter.
The Morley and Outwood MP said: “I stand united with over 30 colleagues who are concerned with the direction of the Brexit negotiations.
"We must be clear to those in the Cabinet, and on the back benches, that we will not sit back and allow a small minority to dominate the agenda. No one must be allowed to undermine the democratic vote of the people.
"Morley and Outwood voted to leave the EU. 59.8 per cent of people in my constituency and 57.7 per cent of Yorkshire and The Humber voting to take back control of their money, laws and borders. We must get tough with the European Union and demonstrate that we are prepared to walk away.”