The proposers of hi-tech solutions to avoid Irish border checks after Brexit, backed by Boris Johnson, have admitted they have no idea what they would cost.

Quizzed by MPs, the head of the Prosperity UK think-tank denied the annual bill would be £13bn, but acknowledged: “We don’t have a figure.”

The stance was criticised by one MP on the Commons Northern Ireland committee, independent Syliva Hermon, who told Shanker Singham: “Somewhere you must have made a calculation of the cost?”

Mr Johnson has made so-called “alternative arrangements” to solve the border controversy a key plank of his promise to renegotiate Theresa May’s divorce deal.

On Monday, the Tory leadership favourite insisted there were “abundant” technical solutions, but “no single magic bullet”, to settle the issue.

Prosperity UK, funded by a Brexit-supporting hedge fund manager, has already acknowledged the plan would take up to three years to implement – so would not be ready for a no-deal Brexit in October.

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

It would also require the EU opening up computer systems, to prevent VAT fraud, and argues for the Irish Republic to shifts food and animal standards from EU to UK rules – both of which are likely to be opposed.

The report, published on Monday, is seen as crucial to Mr Johnson’s attempts to strike a new divorce deal, taking out the flashpoint Irish ‘backstop’, which would tie the UK to EU customs rules.

Mr Singham admitted “there are costs” to the blueprint and argued there would need to be a “transitional adjustment fun for small traders”.

He defended the absence of a cost, telling the committee: “Our job, in the last four weeks, was to come up with the arrangements that we think will makes sense.”

And he added: “Many of the things we are suggesting here do not impose a significant cost because they are electronic procedures, many of which people are already doing.”

Mr Singham pointed to a “trusted trader” proposal, which would remove the need for many checks, adding: “It’s not just a question of imposed costs, there are a lot of savings.”

But he was warned, by Simon Hart, the committee’s Conservative chairman, that the full report – due next month – would be undermined if it failed to include costings.

“I think it could potentially weaken the efficacy of what you are saying unless there is some pounds, shillings and pence,” Mr Hart said.

The interim report, co-chaired by Conservative MPs Nicky Morgan and Greg Hands, argues there is no need for the kind of futuristic high-tech systems branded “unicorns” by critics.

But Owen Smith, the former Labour shadow Northern Ireland Secretary said the “vague” proposals amounted to no more than “a desperate attempt to make a square peg fit into a round hole in order to try and hold the warring factions of the Conservative Party together”.