Leading Brexit supporters have urged the prime minister not to settle the UK's "divorce bill" unless the EU agrees to a series of conditions.
The Leave Means Leave group, which includes ex-cabinet ministers, says Brussels must end the European Court of Justice's jurisdiction over the UK.
It also wants freedom of movement to the UK for EU citizens to stop when Britain leaves the bloc in March 2019.
Theresa May is to hold more meetings next week on the terms of the UK exit.
The UK is hoping to move on to talking about trade but the EU will only do this when it deems "sufficient progress" has been made on three areas – the so-called divorce bill, the rights of EU citizens in the UK after Brexit and the Irish border.
The prime minister has said discussions were continuing over the amount the UK will pay to meet obligations arising from its membership but has already indicated ECJ rulings will apply during a planned two-year transition period.
Signatories of the Leave Means Leave letter to the prime minister include former Tory cabinet ministers Owen Paterson and John Redwood, senior Conservative MP Jacob Rees Mogg, Labour MP Graham Stringer, and entrepreneurs such as Luke Johnson, Tim Martin and Peter Hargreaves.
They say Mrs May should make clear to European Commission President Jean-Claude Juncker and chief Brexit negotiator Michel Barnier "that nothing is agreed until everything is agreed".
The UK should be prepared to revert to World Trade Organisation terms if a future free trade agreement with the EU is not secured, they add.
Leave Means Leave says the UK should not make any payment to Brussels unless the conditions are met.
These also include the UK and the EU agreeing a reciprocal free trade deal without tariffs by the end of March next year and an assurance that no new EU regulations should apply after March 2019.
"If EU negotiators agree to these criteria during negotiations in December, then Britain should make a reasonable, realistic and not extortionate goodwill payment," the letter says.
Last week it was reported that the UK has offered a larger potential "divorce bill" to the EU – which could be worth up to 50bn euros (£44bn).
Meanwhile, the Sunday Telegraph reports that Sir Richard Aikens, a former Court of Appeal judge, has written to Mrs May urging her not to accept a Brexit deal which could see the European Court of Justice continue to issue rulings binding on UK courts.
In an article in the Telegraph, former Tory leader Iain Duncan Smith also says such a plan would be "quite unacceptable… and put the UK in the position of ceding power to a foreign court on which it has no representation to rule on those who would and should normally have their rights adjudicated by British courts".