A NO deal Brexit can only be stopped if MPs come together around “a positive majority for another solution”, Michel Barnier has warned.

The comments by the EU’s chief negotiator appeared to suggest Brussels would resist extending the two-year negotiation process under Article 50 simply to allow the UK to continue debating its preferred outcome.

The prospect of Britain seeking to remain in the EU beyond the planned date of March 29 was increased after Shadow Chancellor John McDonnell signalled Labour could back plans for an Article 50 extension to stop no-deal, a move supported by the SNP. Barnier repeated his position the EU was ready to pursue a more “ambitious” future relationship with the UK if May “modifies” her red lines, which include departure from the customs union and single market, an end to free movement and withdrawal from the jurisdiction of the European Court of Justice.

“If the UK red lines were to evolve in the next few weeks or months, the Union would be ready immediately and open to other models of relationships which are more ambitious,” he said. “Each of these models is founded on a balance between rights and obligations.

“We are open to reworking, if the UK were to modify its red lines, the content and the ambition of the Political Declaration.”

However, there has been no sign of May modifying the red lines and instead hopes to gain EU concessions on the Irish backstop, which would see the UK remain tied to EU rules in the absence of a future trade arrangement keeping the open border.

The EU has insisted the backstop is not open to negotiation.

Speaking to the Eurosceptic Bruges Group in London, arch Eurosceptic Jacob Rees-Mogg denounced efforts to put Parliament in charge of the Brexit process as a “constitutional outrage”. He also played down suggestions members of the European Research Group, which he chairs, might be giving up their rebellion against May’s withdrawal agreement. Restating his opposition to the backstop arrangement, he said: “As long as the backstop is there I will not vote for this deal. Of course any deal would be better than not leaving at all, but this deal ... is not good enough. It needs fundamental change.”

McDonnell said it is “highly likely” Labour will back a “sensible” cross-party amendment to provide parliamentary time to pass a bill allowing suspension of the withdrawal process if no deal is found by the end of February. The move, tabled by Labour’s Yvette Cooper and Tory Nick Boles, is one of a number of amendments due for debate next Tuesday.

The developments came as May and Jeremy Corbyn clashed in the Commons, with the Labour leader repeating his call for the PM to rule out a no-deal outcome.