Prime Minister Boris Johnson and European Commission president Ursula von der Leyen have agreed to “go the extra mile” in the continued search for a trade deal.
Here are the main sticking points and how it might be possible for them to be resolved.
The EU wants to continue to maximise access to UK waters for its fishing fleets after December 31.
The British argue the UK is now an independent coastal state and should be able to prioritise its own boats.
However, most fish caught by UK fishermen are sold in Europe and Britain needs to maintain access to EU markets – suggesting a deal may be in both sides’ interests.
In the end, it will come down to a compromise about how much access EU boats are allowed, what share of the quota they are allowed and the length of time they are given to adapt to the new arrangements.
The level playing field
The so-called “level playing field” rules are intended to ensure businesses on one side do not gain an unfair advantage over those on the other side.
In return for continuing access to the single market, the EU is seeking a high degree of alignment by the UK with its standards on workers’ rights, the environment and state aid for businesses.
While the Government has indicated it will not undercut existing standards, ministers are furious about EU proposals for a “ratchet” mechanism which could result in punitive tariffs being imposed if the UK does not follow suit whenever Brussels imposes new regulations.
Mr Johnson has complained that would leave the UK being treated as the EU’s “twin” and it is a condition no prime minister could accept.
A possible compromise could see the EU drop the demand to automatically impose punitive measures if the UK’s standards fall below those set in Brussels, instead relying on an agreed dispute resolution mechanism.
The two sides are still at odds over the mechanisms for enforcing any agreement and resolving disputes.
The British have been adamant that the UK is an independent sovereign state and cannot accept the jurisdiction of the European Court of Justice.
Brussels is nervous about the UK’s adherence to any deal after Mr Johnson’s threat to break international law by ripping up the already-signed Withdrawal Agreement.
The withdrawal of those measures has eased the tensions, but suspicion still lingers.