The UK and the EU have both agreed “new momentum” is needed to get trade negotiations back on track.
Boris Johnson said he believed there was a “very good” chance of striking a trade deal with Brussels as he insisted the two sides are “not that far apart”.
The Prime Minister called for an agreement to be reached by the end of July after talks with the EU’s leaders.
But European Council chief Charles Michel said the EU would not be pressured into buying a “pig in a poke” and insisted Brussels would stand by its demands for the UK to agree to a “level playing field” to ensure fair competition.
Speaking in Downing Street, Johnson said he believed a deal would be concluded by the end of the year when the current transition arrangements expire “provided we really focus now and get on and do it”.
He suggested the EU wanted to drag the talks out in an attempt to push them towards the December 31 deadline.
It was “very clear what the UK needs” from the deal, he said, adding: “We can’t have the involvement of the European Court of Justice in this country, we can’t have a system whereby we continue to have to obey EU law even when we’re out of the EU and we’ve got to get a great deal for our fish.”
Four rounds of negotiations have so far made little apparent progress, but the two sides have agreed to an “intensified” timetable for talks in the weeks ahead.
Johnson said: “I don’t think we’re actually that far apart, but what we need now is to see a bit of oomph in the negotiations.”
The EU has formally accepted that the UK would not seek any extension to the transition which allows Britain continued access to the single market this year while talks continue.
In a joint statement, the two sides said the earlier rounds of talks led by the Prime Minister’s chief Brexit negotiator David Frost and his EU counterpart Michel Barnier had been “constructive” but “new momentum was required”.
In a video conference the leaders agreed plans to “intensify the talks in July and to create the most conducive conditions for concluding and ratifying a deal before the end of 2020”.
They added: “This should include, if possible, finding an early understanding on the principles underlying any agreement.”
The EU side was represented in the summit by Michel, European Commission president Ursula von der Leyen and European Parliament president David Sassoli.
Michel underlined the EU’s commitment to the “level playing field” – a key demand aimed at ensuring fair competition by preventing the UK straying too far from Brussels’ rules on workers’ rights, environmental protections and state subsidies.
The government has resisted the demand, arguing that it limits the UK’s sovereignty and goes further than conditions imposed on other countries the EU has signed trade deals with.
Michel said a “broad and ambitious” agreement was in both sides’ interests but the level playing field was “essential”.
The EU was “ready to put a tiger in the tank but not to buy a pig in a poke”, he added.
The UK side had originally indicated the Prime Minister could walk away from talks after the June summit if there was no prospect of a deal.
Following the video conference talks with Brussels, Johnson said he believed a deal could be done but “the faster we can do this the better”.
Asked about the possibility of a “cut-off date” on the talks to give businesses some certainty about what to expect from January 1, the PM said: “What we already said today is the faster we can do this the better, we see no reason why you shouldn’t get that done in July.
“The issue is very clear, we fought an election based on these ideas, the manifesto was very clear.”
He added: “I certainly don’t want to see it going on to the autumn or winter as I think perhaps in Brussels they would like.”
Johnson was joined at the virtual summit by Cabinet Office minister Michael Gove, Mr Frost and the UK’s ambassador to the EU Sir Tim Barrow.
A series of weekly talks with the EU will now take place at official level for five weeks, commencing on June 29, looking at detailed technical issues.