LONDON -- British chief Brexit negotiator David Frost said Thursday night that the European Union (EU) and Britain still have "significant" differences over a free trade deal, and their talks will continue in Brussels next week.

Frost made the statement after the latest round of UK-EU trade talks had ended in London without agreement.

The EU warned Britain of legal action over a controversial trade bill, known as the UK Internal Market Bill which was published by the British government on Wednesday. The bill is believed to override elements of British Prime Minister Boris Johnson's Brexit deal with Brussels.

The UK Internal Markets Bill is intended to ensure Northern Ireland can continue to enjoy unfettered access to markets in the rest of Britain. It was published after Britain brushed aside warnings from the EU.

The bill will be formally debated by MPs in the British parliament for the first time on Sept. 14.

In separate hastily arranged talks in London on Thursday, European Commission Vice President Maros Sefcovic demanded Britain withdraw the new bill "by the end of the month" or risk jeopardising trade talks.

Sefcovic said the divorce deal is "a legal obligation" and any action violating the Withdrawal Agreement would break international law.

However, British Cabinet Office Minister Michael Gove, who met with Sefcovic in an emergency joint committee meeting, made it "perfectly clear" that London was not prepared to back down.

"I made it perfectly clear to vice president Sefcovic that we would not be withdrawing this legislation. He understood that. Of course he regretted it," he told reporters after their meeting.

The EU said the on-going situation had "seriously damaged trust" and it would take legal action against Britain. EU chief negotiator Michel Barnier said after the latest round of negotiations that "trust and confidence are and will be key" in the talks.

Britain left the EU at 23:00 GMT on Jan. 31, but that is not the end of the Brexit story because Britain is now in a transition period lasting for 11 months, which keeps the country bound to the EU's rules.