They number more than enough to trigger a leadership bid against May, whose government lacks a parliamentary majority.
The letter sets out the MPs' "continued, strong backing" for the vision set out in May's Lancaster House speech in January 2017.
He claimed the points strengthen "the Government's negotiating position" and underline "that we are not going to be a rule-taker, we are going to be a rule-maker".
The letter from the European Research Group says the United Kingdom should be free to negotiate and sign trade deals with other countries as soon as it leaves.
The idea that the United Kingdom could threaten to withhold the cash risks reopening the argument over money that almost wrecked the first stage of Brexit negotiations past year.
Labour said the letter exposed the "deep divisions" in the Conservatives over Brexit, and accused Mrs May of being "too weak" to confront the Brexit "fanatics" in her own party.
It contains no "pushback" on European Union demands for free movement of people to continue in the same form during the transition phase, no suggestion of a veto to block new European Union laws and no power to implement new worldwide trade deals without the EU's permission, he said.
The European Research Group is seen as an influential Eurosceptic voice within the Tory party.
"The PM has said "up to two years" as have all her Brexit ministers".
The lawmakers' letter was dated February 16.
Shadow Brexit Minister Paul Blomfield said: 'It is clearer than ever that Theresa May can not deliver the Brexit deal Britain needs.
Speaking in Vienna on Tuesday, Davis proposed that so-called "mutual recognition" of regulatory standards should continue after the divorce, to allow cars manufactured and approved for sale on one side of the channel to be approved for sale on the other.
The transition period is due to kick in as the United Kingdom leaves in March 2019, and is meant to give time to prepare for the long-term post-Brexit arrangements between the United Kingdom and the European Union, which have yet to be agreed, and to give businesses time to adapt.
New government proposals say the transition period should last as long as it takes to "prepare and implement the new processes and new systems".
While the letter stopped short of telling May to drop her transition plan altogether, what it called for is quite different from the "no change" period that May and her ministers have told businesses they can expect next year.
"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.