European Commission boss Ursula von der Leyen said that “there is a path to an agreement now”, revealing that UK negotiators had agreed to be bound by the EU in several key areas in perpetuity, but that finalising an arrangement on fishing remains.

A Brexit deal may now be struck within days, even before the end of this week, after two major areas of contention of talks appear to have been resolved, if the EU’s account of events are to be believed.

Speaking to the European Parliament on Wednesday morning, the European Commission’s president said there had been a “big step forward” on what Brussels euphemistically calls the “level playing field” requirement it insists upon in return to agreeing on a trade deal with Britain.

The level playing field are rules on competition that seek to prevent Britain from setting its own regulations after Brexit to suit itself and finding a new competitive edge as an independent sovereign state. The European Union wants Britain to change its own laws in imitation of the European Union’s rules as they evolve over time, in what von der Leyen called future-proofing “fair competition”.

How much ground British negotiators appear to have given was illustrated in her remarks when she said that “on standards we have agreed a strong mechanism of non-regression, that’s a big step forward”.

The purpose of this, von der Leyen said, was to ensure that Britain would be banned from ‘undercutting’ the European Union in future — guaranteeing a straightjacket of EU regulations being imported to London from Brussels in perpetuity. The EC president also said she had extracted “guarantees of domestic enforcement” — preventing the British government from supporting British business should it be required — again, to prevent British businesses from becoming too competitive against European.

Europe also continues to pile pressure and threats upon the United Kingdom to take the deal it is offering now — open borders for trade in return for European political control. Britain’s The Sun reports that Brussels’ chief negotiator Michel Barnier has warned that if no deal is reached by the end of this year, from 2021, negotiations could continue but in a “sector-by-sector” fashion which would see talks dragged out for several years.

The paper reported that Barnier cited the EU’s talks with Canada, which took five years.

Despite the positive noises coming from Brussels, Boris Johnson’s government has moved to reassure British Brexiteers that they won’t be disappointed by the deal that now appears to be coming, reports Westminster gossip blog Guido Fawkes. Their report cites the remarks of a Westminster insider who notes that “Eurosceptics being reassured they will be happy” and that a compromise has been agreed on the level playing field by creating a joint dispute mechanism, rather than the EU being able to unilaterally punish Britain for being perceived to have diverged from European rules.

The Times reported the comments of an unnamed Westminster source who said: “We’ve made some progress but we are still very far apart in key areas.”

The government is also priming Parliament to be ready to vote on a deal at very short notice. While Parliament would normally go into recess before Christmas until the New Year, Jacob Rees-Mogg — the government’s go-between to Parliament itself — cited past precedent of times where very major votes were considered and passed in a single day and Parliament may be asked to sit in Christmas week to vote, if necessary.