UK Prime Minister Keir Starmer is hosting EU chiefs at a summit on Monday, the first of its kind since Brexit, as he tries to deepen relations with the bloc.
Here are the main issues at stake, with sensitive details still being thrashed out in hardball negotiations that are set to go down to the wire.
Defense pact
Both parties are hopeful of reaching agreement on a security deal as Europe races to rearm over fears about Russian aggression and that President Donald Trump is uncommitted to protecting the continent.
The deal would allow Britain to attend certain ministerial meetings and take part in some European military initiatives and missions.
It would also aim to further involve the British defense industry in European efforts to develop its own military industrial base, benefiting UK defence companies such as BAE Systems and Rolls-Royce.
The deal could lead to London accessing a 150-billion-euro ($167-billion) defence fund being set up by the bloc although a further agreement would be needed to give Britain's defence industry full access to the EU programmes.
Fishing
Discussions have been complicated by some EU countries, including France, working behind the scenes to link the signing of the defense partnership to the renewal of an agreement giving EU fishing boats access to British waters.
EU foreign affairs chief Kaja Kallas voiced confidence this week that fish quotas do not need to be agreed before penning the security deal.
But negotiations on this point were heading for the eleventh hour, with EU diplomats yet to sign off on the compromise being drawn up by the European Commission.
The current five-year fishing agreement expires in 2026.
EU countries want the agreement rolled over, in return for slashing red tape for British food exports -- a key item on London's wish list.
But Britain is understood to be offering four more years of access to its waters, less than hoped for on the EU side -- which may seek to curtail the food checks deal as a result.
Standards
Starmer has suggested the UK is ready for dynamic alignment with EU standards on food and agricultural products to ease trade between Britain and the bloc.
The goal is to reduce the burdensome bureaucracy associated with inspecting different products, which hinders the smooth flow of goods.
"I think that British people are proud of the high standards that we have, and we want to maintain those standards," the prime minister told the Guardian recently, referring to regulations mostly inherited from the EU.
The newspaper also reported that he accepted that the European Court of Justice would be involved in resolving disputes.
He pointed out that it already ensures the proper implementation of an existing agreement governing the control of goods between Northern Ireland, which is in the UK, and neighbouring Ireland, an EU country.
Youth mobility
This is the key last-minute sticking point along with fish.
The EU last year proposed a scheme that would allow British and European 18- to 30-year-olds to study and work in the UK and vice versa.
Starmer's Labour government initially rejected the idea but is now open to a possible controlled programme that does not increase the UK's net migration numbers.
According to the Times newspaper, this could mean a "one in one out" policy that caps the number of participants. It would also be time-limited.
Starmer is trying to cut immigration in the face of soaring support for arch-Eurosceptic Nigel Farage's anti-immigration Reform UK party, which made big gains in recent local elections.
London is believed to have refused an EU request to lower university fees paid by EU students to align with the rate paid by their British counterparts.
By Anne-Laure Mondesert with Emma Charlton in Brussels/AFP
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