Raoul Ruparel, a former Europe adviser to ex-prime minister Theresa May who remains well connected in Whitehall, suggested the EU and the UK could find a solution to one outstanding issue holding back a deal: the bloc’s fishing rights in British waters after Brexit. The prime minister’s allies meanwhile said any trade deal struck now would probably have to be voted on by MPs and peers between Christmas and new year, with an emergency parliamentary session being planned.

Britain’s chief negotiator David Frost and his EU counterpart Michel Barnier are haggling over cuts to fishing quotas for EU boats operating in UK waters after Brexit and over the length of any transition period for the industry. Mr Ruparel suggested in an article for Politico that a compromise on fisheries could involve the EU’s rights in UK waters — currently worth around €650m per annum — being cut by 35 per cent over a five-year transition period.

The EU in recent days has offered a 25 per cent cut over a six-year transition — a proposal that France is deeply uncomfortable with and that has prompted outrage from the bloc’s fishing industry. Several people close to the talks on the EU side said their understanding was that the current UK position on quotas and the transition was close to Mr Ruparel’s proposal. British officials denied the UK had made a new offer along the lines suggested by Mr Ruparel, saying only that the two sides were “far apart” and that the negotiations were “brutally complicated”.

Mr Ruparel also proposed a mechanism for addressing EU concerns about what should happen after the fishing transition period if the UK insisted on further big quota cuts: the possibility of the bloc imposing tariffs to recoup any economic loss, with that cost to be determined by an arbitration panel. In extremis, he suggested, the EU could pull out of any trade agreement, which would include a termination clause.

Mr Barnier said last week that some system would be needed to link the EU’s future fishing rights in UK waters to Britain’s access to the bloc’s single market, saying it was a matter of fairness. Mr Johnson’s spokesman said “significant differences” remained between the two sides, with fisheries and a so-called level playing field for fair business competition being the outstanding issues.

But the atmospherics appeared to improve on Monday after Mr Johnson held what he said was an “excellent conversation” with French president Emmanuel Macron.