Health Secretary Jeremy Hunt spoke out on the eve of Mrs May’s trip to meet European Commission President Jean Claude-Junker in Brussels where she is expected to make an final offer on the three Brexit sticking points.
If the European Council rejects the offer on the Irish border, the Brexit settlement and EU citizens’ rights, talks could be stalled until March 2018, giving Britain just one year to make a deal before exiting the bloc.
Health Secretary Jeremy Hunt warned Britain not to underestimate Mrs May.
Mr Hunt was questioned by ITV presenter Robert Peston over whether or not the European Court of Justice will influence Britain after Brexit.
The Health Secretary, who claimed it is perfectly acceptable to look at former ECJ rulings or refer cases when there is no precedent in the UK, said British courts will decide on British cases.
He said: “The choice we face now is not between this Brexit and that Brexit – if we don’t back Theresa May we will have no Brexit.
“She is doing an unbelievably challenging job, amazingly well, but these are negotiations and there are technical things we have to sort out and the fact is that the ECJ will not have sway over British law.”
Mr Hunt said it is common sense to have a deal linking both sides, despite some Brexit politicians saying the UK could leave without a deal in place.
He said: “We have to accept that, in terms of migrants rights for example, we have lots of Brits living in Spain and lots of EU citizens living over here.
“There is going to have to be some kind of co-operation between the legal systems in the UK and the EU to work. But this is a detail, the big thing is that European law will not hold sway over British law.”
Mrs May will travel to meet Mr Juncker tomorrow to make Britain’s final offer which insiders say could include an offer of up to £60n to settle Britain’s so-called contributions until 2020.
The Prime Minister is also expected to propose giving Northern Ireland new powers over borders to avoid a hard border in Ireland, between Ulster and the Republic.