Andrew Bridgen, who was one of the MPs who signed the letter, told Good Morning Britain the piece was not an attempt to hold May hostage.
Other signatories include Bridgnorth-based Eurosceptic Sir Bill Cash, who is MP for Stone, North Herefordshire's Bill Wiggin, and Walsall North MP Eddie Hughes.
Ahead of a planned speech about Brexit later this week, May has called her senior ministers to a meeting at her official country retreat, Chequers, to discuss the government's strategy.
The speech provides "assurances that the government wants to maintain and improve standards that deliver for consumers, whilst not inflicting any additional administrative burden on business", said Helen Dickinson, chief executive of the British Retail Consortium.
"To avoid the perversion of democracy that Brexit in name only would be, it is essential that we are able to sign trade deals in the fixed transition period".
The group promise their "continued, strong backing" for the vision of leaving the European Union set out by the prime minister in her Lancaster House speech in January previous year, but add a list of suggestion about how she could maintain those guarantees.
The letter, co-ordinated by former minister John Penrose, continued: 'Leaving them both isn't a question of ideology but practicality - we can't strike those free trade deals if we don't'.
Responding to Sir Bill at a hearing of the committee, United Kingdom ambassador to the EU Sir Tim Barrow said: "While there has been some discussion in Brussels among the 27 about the duration, the (EU) negotiating directives point to end 2020 and that is the basis on which we are now talking to the commission about the logic of how they derive that figure".
The U.K. opposition leader confirmed his Labour Party will campaign to keep Britain inside a customs union with the European Union, calling it necessary for trade and to prevent a hard border with Ireland.
Shadow Brexit Minister Paul Blomfield said: 'It is clearer than ever that Theresa May can not deliver the Brexit deal Britain needs.
Prime Minister Theresa May is facing a potentially unsafe outcry from 62 members of her own party who are demanding a quick, clean break from the European Union, just as she tries to finalize her Brexit plans. "People arriving after March 2019 arrive in different circumstances to those who arrive before March 2019 and can expect their rights to be different as a result".
"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".
But the prime minister's spokesperson played down the significance of the language on the length of the transition period.
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