The British government suffered a fresh Brexit setback in parliament late on Monday over controversial legislation that would have allowed it to override parts of the country's EU divorce treaty.

Members of the unelected upper chamber House of Lords rejected key provisions of the Internal Market Bill, which is designed to regulate trade between all four UK nations.

The government has insisted the bill provides a safety net in case talks for a new trade agreement fail, even though it admits it breaks international law in a "very specific and limited way".

But the Lords voted overwhelmingly to remove clauses relating to Northern Ireland, which will have the UK's only land border with the EU from January 1 and will remain under some of the bloc's rules.

A "no-deal" could complicate the situation on the island and its politically sensitive border between UK-ruled Northern Ireland and EU member Ireland.

Brussels has already initiated legal action over the draft law.

A government spokesman said after Monday's vote that the removed clauses would be reintroduced when the bill goes back to the House of Commons, where Prime Minister Boris Johnson has a comfortable majority.

- 'Pause for thought' -

Top Democrats in the United States, including President-elect Joe Biden, have waded in, warning a US-UK trade deal could be compromised if a "no-deal" jeopardises a hard-won peace.

An open border was a keystone of the US-brokered 1998 Good Friday Agreement that largely ended more than 30 years of violence over British rule in Northern Ireland.

Irish Foreign Minister Simon Coveney said Monday that the election of Biden, who has Irish roots, could lead London to "pause for thought" and ensure Irish issues are prioritised.

The debate and vote came as London and Brussels met again to thrash out a post-Brexit trade deal.

EU chief negotiator Michel Barnier arrived in the British capital late Sunday before another week of talks with his UK counterpart David Frost, as they scramble to find an agreement.

Britain formally left the bloc in January but remains bound by most of its rules until the end of the year under the terms of its divorce.

- 'Robust guarantees' -

Parliaments in London and Brussels need time to ratify any deal struck, leaving scant time for the two sides to find a compromise on key outstanding issues.

These include establishing rules for competition between British and European companies, oversight mechanisms and fishing rights.

Barnier said on Twitter the keys to unlocking the door to a deal were "respect of EU autonomy and UK sovereignty" alongside "robust guarantees of free and fair trade" and "stable and reciprocal access to markets and fishing opportunities".

On Saturday, Johnson and European Commission chief Ursula von der Leyen acknowledged big differences must be bridged after two weeks of "intense" meetings ended last Wednesday.

Von der Leyen vowed both negotiating teams would "continue working hard" while Johnson said they would "redouble efforts to reach a deal".

But neither side has yet indicated that they were willing to make the compromises needed for a breakthrough, with the clock ticking on an expected mid-November deadline.

Britons voted to end decades of EU economic and political integration in 2016 but implementing Brexit has proved immensely difficult ever since.

Initial divorce terms were finally agreed last year, triggering negotiations over a future free trade deal to be in place in time for the new year.

But the coronavirus pandemic strained the already ambitious timetable, while the most divisive issues have stalled the talks for months.

Without a deal, Britain would leave the EU single market and customs union on January 1, triggering immediate and significant barriers to cross-Channel trade and business.

London and Brussels still insist they would prefer to avoid the economic disruption that this would entail.