The next round of talks begins on Monday and will be held face to face for the first time since the coronavirus epidemic.
This week also marks the beginning of five weeks of "intensified" talks.
The meetings will alternate weekly between Brussels and London throughout July and again in late August.
"We think there is a 50-50 chance of a no trade-deal Brexit", said Sarah Hewin, chief Europe economist at Standard Chartered.
But, in a collection of tweets, David Frost, Boris Johnson's negotiator, introduced: "I would like to be clear that the federal government won't agree to concepts just like the one at the moment circulating giving the European Union a brand new proper to retaliate with tariffs if we selected to make legal guidelines suiting our pursuits". "U.K. sovereignty, over our laws, our courts, or our fishing waters, is of course not up for discussion".
"There are big hurdles still and no one is really talking about Northern Ireland at the moment", she said, referring to one of the main stumbling blocks in past negotiation rounds.
"This will remain his first priority.
There is no way member states or the European Parliament would accept this", Barnier told a Eurofi conference.
Britain's finance ministry said both sides are committed to completing the assessments ahead of the summer, and that it should be a straightforward process given they have similar rules. We need to make sure businesses can prepare properly for what will happen at the end of the year.
The EU is much less pressed for time and believes that the vital ratification by the European Parliament and others would require a offer by late October.
Barnier and Frost now lead smaller teams armed with the political authority to break logjams.
He tweeted: "We will go to Brussels in good faith to engage with the EU's concerns".
But he warned: "This needs to be a real negotiation and some of the EU's unrealistic positions will have to change if we are to move forward".
The discussions will start out with a assembly among the two men at 0800 GMT and will carry on throughout the week with shorter classes on the most problematic matters.
This could be either a very broad deal covering all areas of the relationship, as the Europeans want, or a simple trade agreement with small sectoral side deals as sought by London.
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