British Prime Minister Theresa May has cautioned there may be "no Brexit at all" because of lawmakers' attempts to undermine her plan to leave the European Union.

"My message to the country this weekend is simple: we need to keep our eyes on the prize," May wrote in the Mail on Sunday. "If we don't, we risk ending up with no Brexit at all."

Earlier this week two senior ministers resigned in protest at May's plans for trade with the EU after Britain leaves the bloc next March. Tory Brexiteer Jacob Rees-Mogg also called it a "bad deal for Britain."

David Davis, who resigned as Brexit minister six days ago, said May's plan to commit to following EU rules when trading goods would put British democracy "at stake," and kill any chance of a trade deal with the US.

"Tying ourselves to EU regulations in goods without any say would mean that any new innovative UK company using artificial intelligence or biotechnology to develop life-changing products could find itself facing regulation that makes it uncompetitive to the rest of the world," he wrote.

On the other hand, taking a more hardline stance, Trump has advised British Prime Minister Theresa May to "sue" the European Union to resolve the tense negotiations over Britain's impending exit from the bloc.

The American president told reporters Friday at a joint press conference with May that he had given the British leader a suggestion that she found too "brutal."

May said: "He told me I should sue the EU. Not go into negotiation, sue them," and, "What the president also said at that press conference was 'Don't walk away. Don't walk away from the negotiations. Then you're stuck.'"

May also wrote in the Mail on Sunday article that Britain would take a tough stance in its next round of negotiations with the EU.

"Some people have asked whether our Brexit deal is just a starting point from which we will regress," she said. "Let me be clear. Our Brexit deal is not some long wish-list from which negotiators get to pick and choose. It is a complete plan with a set of outcomes that are non-negotiable."

May's Brexit plan would end free movement of people and the jurisdiction of the European Court of Justice in the UK. And if any Remainers in her party vote with Labour to urge her to negotiate a customs union with the EU, she said "this would be the ultimate betrayal of the Brexit vote."

While it seems that Brexit will still be underway, a few spanners have been thrown into the works that may slow down the whole process. It is up to May to maintain support and be able to convince the cabinet of Brexit's supposed benefits, as well as the ability to follow through with them in the long-term. UK markets have been softer on "no Brexit" hopes, riding off increased investor optimism.