Sixty Conservative MPs, including seven ex-cabinet ministers, are calling for Britain to quit the single market and customs union when it leaves the EU.
Writing in the Telegraph, Suella Fernandes MP said only in leaving would the UK "truly be a beacon of international free trade".
Michael Gove, Iain Duncan Smith and Theresa Villier are among her backers.
The government said it would not give a "running commentary" before talks but would aim for the "best possible deal".
It comes as other senior Tories are urging the PM to drop an appeal against a ruling that MPs must vote on Brexit before the process can begin.
The group of 60 Tories - out of a total of 328 Conservative MPs - want Britain to pull out of both the European single market and the customs union, which allows its members to trade without tariffs but imposes common duties on goods imported from outside the bloc.
Ms Fernandes said the 23 June vote to leave the EU had been "an instruction to untie ourselves from EU shackles and freely embrace the rest of the world".
"As was made clear in the referendum campaign, remaining in the EU's internal market like Norway, or in a customs union like Turkey, is not compatible with either of these commitments and doing so would frustrate the will of the electorate."
A government spokeswoman said it was committed to getting a unique deal for Britain, "not an 'off the shelf' solution".
She said: "The government is painstakingly analysing the challenges and opportunities for all the different sectors of our economy.
"The prime minister has been clear that she wants UK companies to have the maximum freedom to trade with and operate in the single market - and to let European businesses do the same here.
"Beyond that, it's not in the UK's interest to give a running commentary on our thinking that could undermine our negotiating position."
Meanwhile, Sir Oliver Letwin, former head of the government's Brexit preparations, and two former law officers said the appeal against a court ruling that means MPs must vote on the UK leaving the EU should not go to the Supreme Court.
Instead, they want ministers to bring a bill to Parliament to start the process of Brexit as soon as possible.
Former minister Sir Oliver told BBC Radio 4's Today programme that the Supreme Court hearing could see ministers' powers outside Parliament curbed.
He said that bringing a bill to Parliament would give the government the ability to trigger Brexit without any constraints on its negotiating power.
'What's the point?'
Former Solicitor General Sir Edward Garnier said Mrs May should drop the appeal to avoid expense and a row about judges' powers, while former Attorney General Dominic Grieve said he could not see the point of continuing with the case.
The government said it would robustly defend its position at the appeal and said: "As the prime minister made clear [on Friday], our work is on track and we remain committed to triggering Article 50 by the end of March next year."
A final judgement from the Supreme Court is not expected until January.