The proposed law, which overrides parts of the Brexit treaty relating to trade in Northern Ireland, has threatened to torpedo already deadlocked trade talks
The chief negotiators for EU-UK trade talks met in Brussels on Thursday to try to avoid a breakdown after London said it would backtrack on Brexit divorce terms.
The EU's Michel Barnier and UK counterpart David Frost held two hours of talks at European Union headquarters with fears rising of a damaging cliff-edge "no deal" at the end of this year.
Afterwards, Frost left without addressing reporters, but a UK spokesman said he had "had useful informal discussions with the EU this week as we seek to reach an agreement by mid-October on our future relationship.
"These covered a broad range of issues and some limited progress was made, but significant gaps remain in key areas, including fisheries and subsidies," he said.
"We will continue to work hard to bridge those gaps in talks next week, without compromising our fundamental position of being an independent country."
Earlier, an EU spokesman had insisted Brussels was still negotiating in good faith, rejecting accusations by Britain's Prime Minister Boris Johnson, who has claimed the bloc has threatened to "blockade" food heading for Northern Ireland.
"Michel Barnier has shown... that even on extremely complex and politically sensitive issues, the commission, indeed the EU, negotiates in perfectly good faith," said Eric Mamer, the EU spokesman.
The negotiators met as Johnson refuses to back down on controversial new legislation that he admits will break international law and which has infuriated Brussels.
The proposed law, which overrides parts of the Brexit treaty relating to trade in Northern Ireland, has threatened to torpedo already deadlocked trade talks.
The British government "probably don't know themselves if they actually want an agreement in the end or a no deal", an EU diplomat told AFP. "Probably a little bit of both."
The diplomat insisted however, that full clarity on whether a deal was possible would not be achieved for "two or three weeks".
Another European diplomat was more optimistic that a deal would be possible, with the trade talks carrying on in parallel to legal and political wrangling over the British bill.
"If we get close to finalising an agreement on a comprehensive FTA, then you also make progress on these latest hiccups and it all falls into place," he said.
The next official round of negotiations, that involve hundreds of negotiators discussing the thorniest topics, will take place in Brussels the week of September 28, although informal contacts will continue next week.