Ireland has dismissed the suggestion that the best solution to the Brexit impasse might be for the country to quit the EU and join the UK.

Leo Varadkar: Brexit has undermined Good Friday agreement Read more

Questioned about the possibility by the BBC Today presenter John Humphrys, Ireland’s Europe minister, Helen McEntee, said it was not contemplating quitting the EU, that polls showed 92% of the population wanted to remain in the bloc, and “Irexit” was not plausible.

She told the Radio 4 programme on Saturday that, in the event of no deal, Ireland was “not planning for the reintroduction of a border”, and urged the UK to honour its commitment to ensure the border remained invisible, as it had since the Good Friday peace deal was signed nearly 21 years ago.

Humphrys said: “There has to be an argument, doesn’t there, that says instead of Dublin telling this country that we have to stay in the single market etc within the customs union, why doesn’t Dublin, why doesn’t the Republic of Ireland, leave the EU and throw in their lot with this country?”

Facebook Twitter Pinterest BBC Radio 4 Today co-presenter John Humphrys. Photograph: Karwai Tang/WireImage

McEntee replied: “To suggest that we should leave? Ninety-two per cent of Irish people last year said they wanted Ireland to remain part of the European Union and in fact since Brexit that figure has gotten only bigger.”

The interview came hours before hundreds of people gathered on the border to protest against Brexit.

The Border Communities Against Brexit group, which placed a mock concrete wall and army inspection post on the border just south of Newry, said they were taking “a stand against Brexit, against borders, against division”.

Facebook Twitter Pinterest A man uses a sledgehammer to knock down a mock border wall during a protest by anti-Brexit campaigners in Carrickcarnan, Ireland. Photograph: Clodagh Kilcoyne/Reuters

“We never want to see a border on this island again,” they said.

The Labour MP Ben Bradshaw tweeted he was “gobsmacked” to hear the BBC suggest “that the solution to # Brexitshambles is for Ireland to leave the EU & rejoin the UK! Such woeful ignorance of history & of modern day Ireland.”

The Irish senator Neale Richmond said this was what Ireland “was dealing with” in commentary in the UK.

McEntee appeared on Today just hours after the Irish taoiseach, Leo Varadkar, raised the prospect of police or soldiers being deployed on the border with Northern Ireland in the event of no deal.

Sen. Neale Richmond (@nealerichmond) A sterling #brexit performance form @HMcEntee as ever, revealing Ireland leaving the EU was somehow seen as a credible solution by Humphrys in his final questions. For the domestic commentators, this is what we’re dealing with...... https://t.co/EOFg0PgQKo

Varadkar’s statement was criticised by rival politicians, including the leader of Fianna Fáil, Micheál Martin, who said it was entirely inconsistent with Ireland’s stance on the border to date.

“When the taoiseach tells an audience in Davos that the army may have to be sent to the border, he is contradicting everything that we have been told (by him and the tánaiste [deputy leader]) about preparations. It is hard to see how this helps our case,” he tweeted.

Aides later said Varadkar raised the possibility out of frustration that Ireland was being blamed for the impasse in Westminster, where opposition to Theresa May’s deal was not exclusively about the Irish backstop.

In an interview with Bloomberg at the World Economic Forum in Davos, Varadkar said Ireland had already compromised, but Britain was looking for more while offering nothing in the way of solutions itself.

Chaotic Brexit could see uniformed border police, says Irish PM Read more

McEntee stuck to that line on the Today programme, saying the UK had given undertakings to ensure there was no return to the borders of the past.

In addition, she said, Ireland would hold the UK to its role as co-guarantor of the Good Friday agreement.

“For some reason the onus [in Brexit] … has been shifted back on to Ireland, that we should compromise, that we are the ones trying to be awkward or difficult.

“We did not vote for Brexit. We don’t believe in it. We respect that it was a democratic decision. We are protecting a peace process. This is not just from an Irish point of view, there is an obligation on the UK to ensure the peace process, the Good Friday agreement is protected and any suggesting that they can walk away from that we simply won’t accept.”