Jacob Rees-Mogg has sparked a fresh row about the status of the Irish border after Brexit after a video emerged in which he suggests a return to checks “as we had during the Troubles”.

The Conservative MP is seen on the footage from the public meeting suggesting the government could “keep an eye on” the border.

“Ireland would not be a free for all. It would be perfectly possible to continue with historic arrangements to ensure that there wasn’t a great loophole in the way people can get into the UK, to leave us in as bad a position as we are already in,” Rees-Mogg says.

“There would be our ability, as we had during the Troubles, to have people inspected. It’s not a border that everyone has to go through every day, but of course for security reasons during the Troubles, we kept a very close eye on the border, to try and stop gun-running and things like that.”

The shadow Brexit secretary, Keir Starmer, was sharply critical of his comments. “This man knows nothing of Northern Ireland,” he said.

Ireland’s deputy prime minister, Simon Coveney, tweeted:

It’s hard to believe that a senior politician is so ill informed about Ireland + the politics of the #Brexit Irish border issue that he could make comments like these. We have left “the troubles” behind us, through the sincere efforts of many, + we intend on keeping it that way. https://t.co/yuZYDFiWOq — Simon Coveney (@simoncoveney) August 25, 2018

Rees-Mogg has previously been criticised for saying he did not need to visit Northern Ireland to understand the challenges Brexit posed for communities on the border.

His comments, earlier this year, were described as arrogant and judgmental by people living there. In an interview with BBC Northern Ireland, he said: “I don’t think my visiting the border is really going give me a fundamental insight into the border beyond what one can get by studying it.”

The Sinn Féin politician Mártín Ó Muilleoir, South Belfast MLA, said Rees-Mogg’s comments on the border after Brexit showed “contempt and complete disregard for the people of Ireland north and south, through the ridiculous suggestion of a ‘technological border’.

“Anyone labouring under the misapprehension that the Tories care a jot about the north is living in a fool’s paradise.”

The status of the Irish border remains one of the toughest sticking points in the UK’s negotiations on a withdrawal agreement with the EU.

Theresa May has said no UK prime minister could accept the EU’s proposal, for Northern Ireland effectively to remain in the customs union and the single market, with the rest of the UK outside – requiring a border in the Irish Sea.

The EU for its part regards Britain’s solution of a “facilitated customs arrangement”as unworkable.

The Cabinet Office minister, David Lidington, acknowledged on Friday that the October deadline once regarded as the end-date for the Brexit negotiations could now slip to November.

Tensions among senior Conservatives in cabinet were also exposed at the weekend, as the Brexit secretary, Dominic Raab, played down the significance of Treasury forecasts suggesting a no-deal Brexit would blow an £80bn hole in public finances.

“I’m always wary of any forecast, because most of them have been proved to be wrong,” he told the Sunday Times.

As May battles to complete a deal, Rees-Mogg is leading a vocal group of Conservative MPs calling on the party to “chuck Chequers”, the negotiating position painstakingly agreed by cabinet at their July awayday.

They are keen to play down the significance of avoiding a hard border in Ireland, which they believe has driven the logic of the push toward a softer Brexit.

Boris Johnson told MPs in his resignation speech, after he rejected the Chequers deal: “We allowed the question of the Northern Irish border, which had hitherto been assumed on all sides to be readily soluble, to become so politically charged as to dominate the debate.”