The UK government has described talks with the EU over the Northern Ireland Brexit protocol as “constructive” but insisted it was not about to cave in on its demands that the role of the European court of justice be scrapped.

Government sources dampened hopes of a breakthrough, saying the two sides were still “far apart on the big issues”.

Talks aimed at breaking the impasse over the protocol designed to avoid a border on the island of Ireland post-Brexit started 10 days ago, with sources close to the Brexit minister, Lord Frost, noting that “we’ve heard some things from the EU that we can work with”.

But on Saturday the government pushed back on reports that Boris Johnson was about to “cave in” on its previous demands over the ECJ, which many see as an attempt to reinforce its image as the hardliners in negotiations.

“The talks this week were constructive and we’ve heard some things from the EU that we can work with – but the reality is that we are still far apart on the big issues, especially governance,” the source said.

“Our position remains unchanged: the role of the European court of justice in resolving disputes between the UK and EU must end.”

UK sources said “substantial gaps” between the two sides remain and warned that “real progress” had to be made in the coming week as the UK intended to make its decision on whether to trigger article 16 imminently.

They warned “solutions must be found rapidly” as the UK was not content with being “stuck in a process of endless negotiation because the issues on the ground in Northern Ireland haven’t gone away”.

The sources said officials had told the EU that reports this week that supplies of Christmas crackers were being prevented from reaching Northern Ireland were “yet another example of why the protocol wasn’t working”.

Last week there were hints from Downing Street that Boris Johnson was prepared to accept a technical role for the ECJ as long as a new independent arbitration panel involving both sides was the first port of call for disputes.

Under this scenario, article 12 of the protocol would be amended to water down the role of the ECJ.

Some believe this is an elegant solution. As such an arbitration model was already agreed in EU-Swiss talks, it would not require another round of tough negotiations to get approval from EU member states.

It could also address the complaint from unionist critics of the protocol over sovereignty.

Experts including Catherine Barnard, professor of EU law at the University of Cambridge, said that in reality disputes over the trade of goods rarely reach the level of the ECJ, with as few as 24 cases pending out of a total 1,045 on the Strasbourg court lists.

A team from the European Commission is due to travel to London on Tuesday for several days of intensive discussions.

Frost and the EU Commission vice-president, Maros Sefcovic, are then due to meet in person in Westminster for talks at the end of the week. The two leaders will take stock and assess progress so far.