The Northern Ireland minister, Steve Baker, is proposing reopening the Brexit trade agreement David Frost struck with the EU as a means of fixing the problems caused by the Northern Ireland protocol. The proposal comes after Rishi Sunak moved to quell a rebellion in the Conservative party over suggestions Downing Street was mulling a Swiss-style relationship with the EU to ease wider trade barriers on food and agricultural products. In a confidential paper circulating in the Northern Ireland Office, Baker outlines potential ways of removing the role of the European court of justice in disputes, something both unionists and the Eurosceptic European Research Group are demanding. The proposals essentially revisit a sequencing argument the UK lost in 2017 while the Conservative party was in disarray over whether to stay in the EU customs union and single market. When it did not get the necessary commitment from Theresa May, the EU decided that the Northern Ireland protocol should be placed in the legally binding withdrawal agreement and not the trade deal. In the paper Baker suggests reversing that sequencing in retrospect to end the row over the Northern Ireland protocol. He suggests updating the trade agreement by adding a “customs cooperation chapter” and changing the protocol to include a dispute mechanism that does not involve the ECJ. But experts say it could be an insurmountable challenge. “All of this is theoretically possible but whether the EU would agree to it is another issue,” said Catherine Barnard, professor of EU law at Cambridge University and deputy director of the UK in a Changing Europe thinktank. She said the EU has “taken a very strong line” that the ECJ has to have a role in the protocol if Northern Ireland is to remain in a halfway house – following both UK and EU rules on trade. “The EU will say until it is blue in the face that because Northern Ireland remains in the customs union, because everything from packaging to things as rarefied as animal semen is subject to EU law the ECJ has to have a role as it is the only arbiter of its own law,” she said. Katy Hayward, professor of political sociology at Queen’s University Belfast, said it was difficult to see the EU revisiting deals that took four tumultuous years of negotiation. “The terms of trade between the UK and EU directly affect the challenges for post-Brexit Northern Ireland, caught as it is between Britain and Ireland. So recognition that the TCA has ramifications for the protocol’s operation is welcome. However, if [vice-president of the European Commission’] Maroš] Šefčovič doesn’t have a mandate to rewrite the withdrawal agreement to fix the protocol, he most certainly doesn’t have one to revise the TCA too. “Although there is scope in both agreements for adjustment by mutual decision between Šefčovič and [UK foreign secretary James] Cleverly, it wouldn’t be enough make substantive changes or add new chapters,” Hayward said. But Baker has been arguing that while it is a “narrow and steep” path, the political will to find a solution to the Northern Ireland Brexit question is there given that the US president, Joe Biden, the EU, Ireland and the British governments have expressed their determination to find a negotiated solution by the 25th anniversary of the Good Friday agreement next April. Under the present arrangements, businesses sending goods from Great Britain to Northern Ireland must comply with EU laws and regulations on customs and standards. The EU has suggested a light-touch express lane for goods that remain in Northern Ireland such as sausages, ready meals and horticultural products including seed potatoes and trees for supermarkets, and garden and farming outlets. The UK has been demanding a similar system with “green lanes” for trucks laden with goods for Northern Ireland and “red lanes” for those with goods destined for the Republic of Ireland and the EU. Šefčovič has recently said this system would reduce checks to a couple of lorries a day. Last year Šefčovič said a Swiss-stye trading arrangement would get rid of 80% of the checks as it would mean food and agriculture standards in the UK were legally aligned with the UK. However, Sunak pushed back on reports that he was now considering this as an option on the wider UK-EU stage, saying earlier this week that having “regulatory freedom” to diverge on EU standards was a key advantage, insisting it would not be sacrificed in any future talks.