The warning by the Parliament raises the possibility that the UK could be hit by a limited period of trading on no-deal terms from the beginning of January, even if an agreement is signed before the end of the year.
While the European Union and UK both have some powers for “provisional” application of deals without the consent of their parliaments, it is not clear whether these would help prevent a no-deal in this case.
Mr Barnier is understood to have told ambassadors and MEPs in separate private meetings that even the reduced length of the provisional application process means there could well be a short no-deal in January even if it is used.
The European Commission president Ursula von der Leyen has also promised the Parliament that she would not use the procedure to bypass MEPs. The joint statement by the parliamentary group leaders recalls this, noting that Ms Von der Leyen said provisional application could take place “only once the European Parliament has given its consent”.
The Independent additionally understands that the European Council’s legal service believes that provisional application would not be fast enough to prevent a no-deal on 1 January if the process was set in motion after this week.
Mr Barnier struck an upbeat tone on the possibility of a free trade agreement on Thursday, saying there had been “good progress” but that “stumbling blocks remain”.
He said talks were in their “final stretch”, adding: “We will only sign a deal protecting EU interests and principles.”
The chief negotiator reporters told presidents that a deal was possible by Friday.
But UK sources were significantly less upbeat, stressing that the two sides were still very far apart in key areas. EU member state diplomats believe a deal is possible but warn that the path to one is narrow.
Back in Westminster, Downing Street would not be drawn on the European Parliament’s timetable. The prime minister’s spokesperson said the House of Commons would not be recalled on Christmas Day or the Boxing Day Bank Holiday for its own ratification procedures, but did no rule out weekend sittings to approve the agreement.