Alister Jack, Stephen Kerr and Colin Clark are among 62 Tory MPs to have put their names to the letter.
That the United Kingdom has "full regulatory autonomy" and isn't constrained by European Union rules after-Brexit - which would be a possible outcome if the government successfully pushes for a close relationship with the organisation.
Jacob Rees-Mogg, the chairman of the European Research Group, met May with some of his colleagues in her 10 Downing Street office on Tuesday to discuss their demands.
"I want to ensure that UK companies have the maximum freedom to trade and operate within German markets, and for German businesses to do the same in the UK", May said after meeting German leader Angela Merkel in Berlin.More news: Apple plans to update AirPods, expand wearable options
The letter backs the vision of Brexit set out in Theresa May's Lancaster House speech given in January 2017, including leaving the Customs Union and Single Market, and insists the Tories stick to their manifesto pledges.
"Your government must have the ability to change British laws and rules once we leave, rather than being a 'rule-taker,"' it said.
Furthermore, "the United Kingdom must be free to start its own trade negotiations immediately", and "any implementation period must not restrain the United Kingdom from negotiating or signing other trade agreements".
"The UK should negotiate as an equal partner". Ministers may not want or be able to accept the EU's timing and mandates as fixed, and should be able to set out alternative terms including, for example, building an agreement based on our World Trade Organisation membership instead.
Any implementation period must not restrain the United Kingdom from negotiating or signing other trade agreements.More news: Former Google employee sues company over discrimination
But what should the millions who backed Vote Leave make of the government's vision?
With no majority, she knows that she needs to keep the dozens and dozens of Brexit-backing Tory MPs broadly with her for her own government's survival. "She is too weak to face down the fanatics in her own party and to deliver a final deal that protects jobs and the economy", said Paul Blomfield, the shadow Brexit minister.
"It appears the Government wants transition to last indefinitely - a never-ending road to nowhere because the Cabinet can't agree on our future trading relationship with the EU".
A "Ransom Note" demanding Hard Brexit comes as the Prime Minister and "Soft Brexiteers" have been hoping to reach accommodation with Brussels.More news: China Probing Possible Breach of UNSC's N Korea Sanctions During Sea Transfer