The letter says the United Kingdom must gain full "regulatory autonomy" after Brexit, and must not be stopped from negotiating trade deals with other countries.
The letter, organised by the European Research Group of euroskeptic Tories, is a potentially destabilizing development at a highly sensitive time for May's Brexit preparations.
If just 15% of Conservative MPs were to write to the chairman of the 1922 Committee of backbenchers, Graham Brady, saying they no longer have confidence in the PM a leadership challenge would be sparked.
In the letter, the MPs say they will only support a transition period - favoured by proponents of a "softer" Brexit, during which Britain would stay within many existing European Union structures.
The members of the European Research Group are pushing for a clean break from the EU with "full regulatory autonomy" outside of the European Single Market.
"We are writing to reassure you of our continued, strong backing for the clear vision of an internationally-engaged, free-trading, global Britain which you laid out", said the letter, before offering "some suggestions" on how to achieve it.
The MPs also insist the United Kingdom must be "free to start its own trade negotiations" during the planned two-year transition period.
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'The UK should negotiate as an equal partner.
"Any "implementation period" should be based on WTO principles".
Any implementation period, should be based on WTO principles, they added, without any obstruction to the United Kingdom from negotiating or signing other trade agreements.
SNP foreign affairs spokesman Stephen Gethins said: "The process for leaving the European Union has been hijacked by hard right Tories whose agenda for Brexit at any costs will be devastating for us all in terms of jobs, the economy and opportunities for young people in the future".
Mr Gethins added: "It is clear from this list of demands that the Tories don't want either a transition deal or a future 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.