Negotiators of a Brexit trade deal inched towards a compromise on fishing rights on Sunday but missed a major deadline, raising the prospect of weeks without arrangements from 1 January even in the event of agreement. The teams led by the chief UK negotiator, David Frost, and his EU counterpart, Michel Barnier, were expected to continue talks on Monday despite the European parliament’s notice that it would not vote on a deal if not secured by midnight on Sunday. A UK government source said: “Teams have been negotiating throughout the day and expect to continue tomorrow. Talks remain difficult and significant differences remain. We continue to explore every route to a deal that is in line with the fundamental principles we brought into the negotiations.” Frost met Barnier on Sunday afternoon to discuss the latest EU proposals on fisheries, with the UK side posing a series of questions to be answered on Monday, raising some hope of progress. The UK health secretary, Matt Hancock, said the talks had been derailed in recent days after the EU “put in some unreasonable demands” on fisheries, but that he was still hopeful of an agreement before Christmas. “I’m sure that a deal can be done, but obviously it needs movement on the EU side,” he said. The failure to meet the European parliament’s deadline means that ministers on the EU council representing the bloc’s capitals may need to “provisionally apply” a deal on 1 January to avoid a no-deal exit until parliament votes later in the month. If the talks go much deeper into December, however, there may not be time for the EU capitals to translate and scrutinise the agreed text, leaving the UK to exit the transition period without new trade and security arrangements with Brussels. Contingency measures would have to be agreed to bridge the gap before a deal could come into force, but such a scenario raises the danger of ports and security services being left in legal limbo. Bernd Lange, the German chair of the parliament’s trade committee, the key body in the chamber’s ratification process, tweeted: “The consequence of no deal tonight is obvious: the [European parliament] does not know the consolidated text, is not in a position to scrutinise before the end of the transition period. So make preparations now for a no-deal period and agree emergency measures with UK.” A major sticking point in the talks remains the EU’s demand to be able to apply tariffs or entirely block the entry of British goods in the event of the government closing off access to UK seas after a transition period to phase in new fishing arrangements for European vessels. Under the British proposal, Boris Johnson insists that UK-flagged vessels have exclusive access to the six-to-12 nautical mile zone off the British coast, fished for centuries by French and Belgian vessels. Such a move would lead to some British exports being kept out of its biggest market under the proposal Brussels has tabled. Barnier tweeted: “In this crucial moment for the negotiations, we continue to work hard with David Frost and his team. “The EU remains committed to a fair, reciprocal & balanced agreement. We respect the sovereignty of the UK. And we expect the same. “Both EU and the UK must have the right to set their own laws & control their own waters. And we should both be able to act when our interests are at stake.” His comments indicate that there has been some movement on the issue, with both sides able to take measures should their interests be threatened, but UK sources downplayed any suggestion of a breakthrough. The exhausted British team in the UK mission to the EU, many of whom have been away from home for the last two weeks, were served mince pies and mulled wine, delivered from the British ambassador’s residence as they worked through Sunday. Clément Beaune, France’s European affairs minister, said he believed a deal with the UK remained doable. “We have given ourselves a few more days because we think that an agreement is still possible,” he said. “It’s hard, not sure, but worth a try. More than an agreement, we want a good agreement, in particular preserving fishing and fair conditions of competition. The negotiations should be concluded in the next few days. We know where our red lines are and what interests we don’t want to sacrifice.” All the political groups in the European parliament apart from the Greens had agreed on the Sunday night deadline for a deal. Philippe Lamberts, the co-leader of the Greens, said: “The position that we defend is that negotiators should be allowed to work until the last minute, and simply give us time in January and February to scrutinise and ratify any deal. I’m watching quite gleefully, I must say, because I was quite angry at my colleagues and now they will look stupid.”