Boris Johnson has hinted he may not support a proposed deal over the Northern Ireland protocol from Rishi Sunak, heaping pressure on the prime minister to revive a controversial bill that would unilaterally override parts of the Brexit treaty.

His intervention came on Thursday as it emerged that lawyers advising Eurosceptics in the Conservative party submitted fresh proposals to Sunak to end the rule of EU law in Northern Ireland, one of the major sticking points in the UK-EU negotiations over the protocol.

The proposals were sent to Downing Street, senior ministers and the European Commission as the Northern Ireland secretary, Chris Heaton-Harris, travelled to Brussels for more talks with the commission vice-president Maroš Šefčovič.

In an interview with Sky News, Johnson said it was “important that we wait to see what there may be” in Sunak’s deal. But the former prime minister went on to say: “I think the best way forward, as I said when I was running the government, is the Northern Ireland bill, which, you know, cleared the Commons very comfortably, I think unamended, when I was in office only a few months ago. So I think that’s the best way forwards.”

The bill, which would allow the UK to unilaterally rip up some Brexit arrangements for Northern Ireland, has been paused amid the EU-UK discussions.

Johnson said: “It’s a very good bill. It fixes all the problems. It solves the problems that we have in the Irish Sea, solves the problems of paperwork, VAT and so on. It’s an excellent bill and doesn’t set up any other problems in the economy of the whole island of Ireland. So I’d go with that one.”

The bill would allow the UK government to ignore parts of the protocol disliked by traders with Northern Ireland, but critics say that this would breach international law and that, if the UK government ever tried to use it, the EU could retaliate by imposing tariffs on imports from Britain.

The proposals to Sunak from Eurosceptics’ legal advisers suggested a system that would mean any businesses exporting to the EU that breached European regulations would be prosecuted in British courts rather than the European court of justice.

To work, the government would pass special legislation creating a new export certification and tariff collection system for exporters to the EU. By signing up to the certification, exporters in Northern Ireland would agree to pay tariffs if applicable and follow all EU laws relevant to their products.

The Democratic Unionist party told the BBC on Wednesday night: “Sir Jeffrey [Donaldson, the DUP leader] did not approve this document but was advised it was being sent.”

It is understood the document, seen by the Guardian, was written by some senior figures in Lawyers for Britain – a group of lawyers and academics who backed the leave campaign and are part of the European Research Group of Eurosceptic Tory MPs’ “star chamber” of legal advisers – along with Jamie Bryson, the Northern Ireland policy director at the Centre for the Union thinktank.

Christopher Howarth, an adviser to the ERG, told BBC Northern Ireland’s Nolan Live: “When we saw this proposal we thought it was incredibly interesting because it raises a way of solving the problem of the Northern Ireland protocol in a way we think could solve the needs of all the major parties to it – the EU and Ireland’s needs, the needs to remove EU law and [create] democratic consent in Northern Ireland – and do it in a way that leaves an invisible border, and non-compliant goods don’t get into the EU’s market.”

Both the DUP and the ERG stressed they were not authors of the document but Howarth told Nolan Live he had discussed it with Donaldson. “I have discussed this with him and I think he would share the view that it is a very interesting proposal that deserves to be discussed because it is a potential solution,” Howarth said.

Under the proposals, British prosecutors could take companies in Great Britain to court if they were sending components to Northern Ireland that failed to comply with EU law but ended up in finished products exported from the region to the single market.

“EU law would not itself directly apply within the territory of Northern Ireland, and would only arise at or beyond entry to the Republic [of Ireland], at which point EU law could be enforced by the EU/Irish government,” says the letter.

The document suggests the EU and Ireland would apply a similar system in reverse with their own export certification to comply with UK law.

Under the system, companies in Great Britain sending products, including components, to Northern Ireland that would end up being exported to the EU, would have to go through “red lane” checks in transit on the ferry or on arrival at the port in Belfast or Larne.