Michel Barnier said there were disagreements around fair competition, cooperating over crime and fishing.
London and Brussels have many "very serious" differences over their future relationship, according to the EU's chief Brexit negotiator.
Michel Barnier, speaking on Thursday after the first round of talks, said there were disagreements around fair competition, cooperating over crime and fishing.
On fair competition, Barnier said London claims to have "ambitions of high standards" but "do not want to translate these commitments into a common agreement".
"The United Kingdom wishes to have a suite of agreements a series of sectoral arrangements on a case by case basis where they think it's necessary. We do not understand since we're working on all these subjects in parallel.
"Why not put our relationship into a global framework?" he said, insisting that it was a "practical point".
Law enforcement cooperation
Barnier spoke about cooperating on law enforcement.
He said that "ambitious cooperation... requires commitment from both sides with respect to the fundamental rights of persons".
"Yet the United Kingdom informs us that they do not wish to commit formally to continuing to apply to European Convention nor do they wish for the European Court of Justice to play its full role in interpreting European law."
This, he said, would create a problem for sharing data such as DNA for cooperation in this domain.
"This is a must-have for us... I say this is grave because if the United Kingdom's position does not move it will have an immediate and concrete effect on the level of ambition of our cooperation," Barnier said.
The last point Barnier covered was a disagreement on fisheries, which it wants to negotiate reciprocal access on an annual basis.
"A trading agreement, a commercial agreement, an economic agreement will have to include a balanced solution for fisheries," he said.
"Our fishing waters are our sovereign resource, and we will determine other countries' access to our resources on our terms," Cabinet Office minister Michael Gove told the House of Commons recently.
The fishing industry had a value of approximately €905 million in the UK in 2018, a number that decreased from previous years.
Barnier also said that there would be "definitive changes" that he says are "underestimated".
They include customs checks and that UK certification "will no longer mean" something can be "marketed in the European Union". He said these were consequences of the UK leaving the customs union.
"Nobody contests the UK's independence. And we as the UK to respect our own independence," Barnier said.
Watch Michel Barnier's news conference from Thursday (March 5) in the video player, above.