Ministers say a planned "status quo" period after Brexit will end on a "fixed date" despite critics suggesting it could "last indefinitely".
Any implementation period must not restrain the United Kingdom from negotiating or signing other trade agreements.
The leaked plans say there are "only a small number of areas" where the two sides disagree.
In their letter, Tory Eurosceptics including former ministers Priti Patel and Iain Duncan Smith warned the United Kingdom must have full control over laws after Brexit and must not become a "rule taker".
The UK's proposals are due to be officially published later, and the BBC's Norman Smith said much of the document would make "uncomfortable reading" for Tory Brexiteers.
"The UK should negotiate as an equal partner".
The opposition Labour party said the letter exposed the "deep divisions" in the Conservative Party.
What is most concerning about the letter - concerning for Leavers like me, or Remainers, or anyone who wants Britain to come through Brexit...
"We also want to share some suggestions for how it could be achieved", they wrote in the letter.
BBC political editor Laura Kuenssberg said the leak suggested the United Kingdom "has softened its position".
The letter, revealed by the Times tonight, urged Theresa May to stick to the Brexit ideals outlined in her rousing Lancaster House speech one year ago.
"The UK must be free to start its own trade negotiations immediately", the letter, organised by the European Research Group, a caucus of Tories wanting a maximum distance from the EU, said.
"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".
"Businesses need to know". It was only last summer that the Home Secretary claimed that the level of encryption on WhatsApp was too much - "real" people don't always want "unbreakable security" from their messaging app, she explained. "Even Tory backbenchers are demanding to know".
The signatories also demanded that the United Kingdom begin negotiating its independent trade agreements immediately rather than after it has withdrawn from European Union institutions. "If there's no trade agreement, guess who is going to suffer the most - it will be the European Union because we're going to open our markets to the rest of the world".