Ken Clarke has urged Tory MPs to ignore an extraordinary warning that defeat on the customs union would topple Theresa May and vote for the “national interest” regardless.

No 10 has piled pressure on potential Conservative rebels by suggesting next month’s showdown will be a “confidence vote”, the BBC reported – meaning defeat would bring down the government.

Such a threat would hugely magnify the importance of the vote – on whether the UK remains in a customs union with the EU after Brexit – and make it harder for Tory MPs to defy the prime minister.

But Mr Clarke accused No 10 of plunging into a “panic of the day”, after Brexiteer MPs demanded that Ms May hold the line, urging fellow pro-EU Tories not to be deflected by the hardline tactics.

“In the end, parliament has to decide what is in the national interest,” the former chancellor said.

The veteran Europhile pointed to the threat of “huge customs barriers and delays” and mounting evidence that leaving the customs union would force border checks in Northern Ireland.

An “absolute red line is we should not break the Good Friday Agreement”, which should not be dismissed as an “inconvenience”, he told BBC Radio 4’s Today programme. “It’s the next big problem and it will need all this to be resolved over the next month or two because it’s got to be – we won’t make much progress until the Irish problem is solved,” Mr Clarke said.

Meanwhile, CBI president Paul Dreschler issued a strongly worded rebuke to Sajid Javid, the communities secretary, after he insisted Britain must leave the customs union.

Brexit threatens life on the Irish border: in pictures Show all 15 1 /15 Brexit threatens life on the Irish border: in pictures Brexit threatens life on the Irish border: in pictures An abandoned shop is seen in Mullan, Co Monaghan. The building was home to four families who left during the Troubles. The town was largely abandoned after the hard border was put in place during the conflict. Mullan has seen some regeneration in recent years, but faces an uncertain future with Brexit on the horizon Reuters Brexit threatens life on the Irish border: in pictures A defaced ‘Welcome to Northern Ireland’ sign stands on the border in Middletown, Co Armagh Reuters Brexit threatens life on the Irish border: in pictures Mervyn Johnson owns a garage in the border town of Pettigo, which straddles the counties of Donegal and Fermanagh. ‘I’ve been here since 1956, it was a bit of a problem for a few years. My premises has been blown up about six or seven times, we just kept building and starting again,’ Johnson said laughing. ‘We just got used to it [the hard border] really but now that it’s gone, we wouldn't like it back again’ Reuters Brexit threatens life on the Irish border: in pictures Farmer Gordon Crockett’s Coshquin farm straddles both Derry/Londonderry in the North and Donegal in the Republic. ‘At the minute there is no real problem, you can cross the border as free as you want. We could cross it six or eight times a day,’ said Crockett. ‘If there was any sort of obstruction it would slow down our work every day’ Reuters Brexit threatens life on the Irish border: in pictures John Murphy flies the European flag outside his home near the border village of Forkhill, Co Armagh Reuters Brexit threatens life on the Irish border: in pictures Potter Brenda McGinn stands outside her Mullan, Co Monaghan, studio – the former Jas Boylan shoe factory which was the main employer in the area until it shut down due to the Troubles. ‘When I came back, this would have been somewhere you would have driven through and have been quite sad. It was a decrepit looking village,’ said McGinn, whose Busy Bee Ceramics is one of a handful of enterprises restoring life to the community. ‘Now this is a revitalised, old hidden village’ Reuters Brexit threatens life on the Irish border: in pictures Union Flag colours painted on kerbstones and bus-stops along the border village of Newbuildings, Co Derry/Londonderry Reuters Brexit threatens life on the Irish border: in pictures Grass reflected in Lattone Lough, which is split by the border between Cavan and Fermanagh, seen from near Ballinacor, Northern Ireland Reuters Brexit threatens life on the Irish border: in pictures Donegalman David McClintock sits in the Border Cafe in the village of Muff, which straddles Donegal and Derry/Londonderry Reuters Brexit threatens life on the Irish border: in pictures An old Irish phone box stands alongside a bus stop in the border town of Glaslough, Co Monaghan Reuters Brexit threatens life on the Irish border: in pictures Billboards are viewed from inside a disused customs hut in Carrickcarnon, Co Down, on the border with Co Louth in the Republic Reuters Brexit threatens life on the Irish border: in pictures Seamus McQuaid takes packages that locals on the Irish side of the border have delivered to his business, McQuaid Auto-Parts, to save money on postal fees, near the Co Fermanagh village of Newtownbutler. ‘I live in the south but the business is in the North,’ said McQaid. "I wholesale into the Republic of Ireland so if there’s duty, I’ll have to set up a company 200 yards up the road to sell to my customers. I’ll have to bring the same product in through Dublin instead of Belfast’ Reuters Brexit threatens life on the Irish border: in pictures A disused Great Northern Railway line and station that was for customs and excise on the border town of Glenfarne, Co Leitrim Reuters Brexit threatens life on the Irish border: in pictures Alice Mullen, from Monaghan in the Republic of Ireland, does her shopping at a former customs post on the border in Middletown, Co Armagh. ‘I’d be very worried if it was a hard border, I remember when people were divided. I would be very afraid of the threat to the peace process, it was a dreadful time to live through. Even to go to mass on a Sunday, you’d have to go through checkpoints. It is terribly stressful,’ said Mullen. ‘All those barricades and boundaries were pulled down. I see it as a huge big exercise of trust and I do believe everyone breathed a sigh of relief’ Reuters Brexit threatens life on the Irish border: in pictures A bus stop and red post box stand in the border town of Jonesborough, Co Armagh Reuters

“An MP of your talent should rise above ideology and lead based of fact, analysis and evidence – all of which favours a customs union. Always happy to discuss,” Mr Dreschler tweeted.

Labour seized on the hints that votes on the customs union could be a “matter of confidence”, pointing that No 10 appeared to rule that out as recently as February.

But Jeremy Hunt made clear the government would not give way, saying: “The prime minister has been totally clear right from the outset. We’re not going to be part of the customs union or a customs union.”

Tensions rose over the weekend, after a Downing Street aide told The Sunday Times that Ms May and her allies “would not be crying into our beer” if parliament forced the government to back down. The scenario was said to have been “war gamed” at a recent meeting, with the conclusion that only Boris Johnson and Liam Fox would resign.

The controversy will come to a head after a heavy defeat for the government in the Lords last week. There will be a non-binding vote in the Commons on Thursday – with a full showdown next month.