Saying that EU respects Britain's sovereign decision to leave the Single Market and the Customs Union, Barnier warned that the Single Market, the EU capacity to regulate, to supervise, to enforce our laws, must not and will not be undermined by Brexit.

"The European Council guidelines state that the Union will preserve its autonomy of decision-making. The UK wants to take back control, it wants to adopt its own standards and regulations. But it also wants to have these standards recognised automatically in the EU. That is what UK papers ask for," Barnier told reporters, calling this as "simply impossible."

"You cannot be outside the Single Market and shape its legal order."

For his part, Davis said Britain remains committed to making as much progress as possible on those issues, "but our discussions this week have exposed yet again that the UK's approach is substantially more flexible and pragmatic than that of the EU as it avoids unnecessary disruption for businesses and consumers."

"We have proposed pragmatic solutions to prevent this disruption and we urge the EU to be more imaginative and flexible in their approach to withdrawal on this point," he added.

Hailing the first phase of this negotiation as crucial to create trust, Barnier said the two sides have not built sufficient trust on citizens' rights and the financial settlement.

"Over the summer, around one hundred EU and EEA citizens living lawfully in the UK received deportation letters...It reinforces the need to ensure that citizens' rights are directly enforceable in front of national jurisdictions, under the control of the European Court of justice, a point on which we disagree today," said Barnier.

"In July, the UK recognised that it has obligations beyond the Brexit date. But this week the UK explained that these obligations will be limited to their last payment to the EU budget before departure," said Barnier, reminding Britain that "we have joint obligations towards third countries."

"With such uncertainty, how can we build trust and start discussing a future relationship? We need to address together these issues seriously and rigorously," he added.

Responding to Barnier's scolding, Davis insisted that "there is an unavoidable overlap between withdrawal and the future and they cannot be neatly compartmentalised."

"The third round of talks have been productive and are an important stepping stone and key building block for discussions to come. We are peeling away the layers, one by one, working through many issues at speed, and moving towards the core of these important matters," said Davis.

"Let's continue to work together constructively to put people above process," he concluded.

Highly anticipated, the third round Brexit talks kicked off on Monday in EU Commission headquarters. There were three negotiating groups covering citizens' rights, financial settlement and other separation issues. The issues related to Northern Ireland and the governance of the withdrawal agreement were addressed by the Coordinators.