Claims by a pro-leave group that a “clean Brexit” – leaving the single market and customs union – could save Britain £450m a week have been described as meaningless by the Liberal Democrats and a leading economist.

Change Britain, backed by the former cabinet minister Michael Gove, Labour’s Gisela Stuart and the former Conservative chancellor Nigel Lawson, released research on Tuesday arguing that a clean break with the EU would be more beneficial to the economy than a soft Brexit.

The group is the successor organisation to Vote Leave, the successful referendum campaign to quit the EU, which claimed that leaving could save £350m a week to go to the NHS, an assertion that was widely criticised.

In its research, Change Britain estimated that there would be £24bn of benefits overall from a clean Brexit, citing savings from ending EU budget contributions, forging bilateral trade deals with new countries and getting rid of some EU laws.

But the former chief economist at the Cabinet Office, Jonathan Portes, said the figure was adding together supposed savings that could not be compared. “Adding increased exports and reduced government expenditure is literally meaningless. The results mean nothing. It isn’t research, it’s junk,” he said.

Another problem with the calculation was counting the benefit of trade deals with countries such as South Korea that already have an agreement with the EU, Portes said.

“But to my mind that is second order. Anybody who adds together increased government revenue literally has no idea what they are doing … It’s no surprise people who backed the fictitious £350m figure also back this number,” he said.

Tim Farron, the Lib Dem leader, also rejected the numbers as “fantasy figures” that no one would believe after Vote Leave’s claims.

“Today’s claims are just the latest in a procession of lies pushed out by the usual suspects who are desperate for a hard Brexit that will rip Britain out of the single market,” he said.

“Leave campaigners spent weeks gallivanting around the UK in a big red bus with a promise of more money for our NHS emblazoned on the side; it was a clear promise to British public who were told that lie over and over again.

“It played on people’s legitimate fears about this government’s underfunding of the NHS. The lie that a leave vote would mean more money for the NHS each week was a disgracefully cynical ploy.

“To now present the public with an even bigger made-up number is shameless and these scaremongers should take a look at themselves in the mirror.”

Change Britain includes former remain supporters, but its founding members are largely made up of those involved in the Brexit campaign, including the Tory donor Peter Cruddas, the former CBI director general Digby Jones and David Owen, the former Labour foreign secretary who went on to help found the Social Democratic party.

Boris Johnson, the foreign secretary and a leading figure in Vote Leave, recorded a video supporting the group’s launch, although he is not formally affiliated.

The Change Britain research suggests many of those linked to Vote Leave do not repudiate the claim that leaving the EU would save £350m a week for the health service, despite it being criticised for failing to take into account the UK’s rebate, the possible budgetary costs of leaving and the lack of any indication that this cash would go to the NHS.

The cabinet is split over the issue of how to approach Brexit, with some of the most hardline members, such as Liam Fox, the international trade secretary, keen to leave the customs union, while others including Philip Hammond, the chancellor, push for an exit from the EU that leaves the UK as close to the single market as possible.

Theresa May has not indicated which type of Brexit she wants to pursue other than to say issues such as the customs union are not a “binary choice” about staying in or out. The prime minister has also made controls on immigration a red line and said she wanted the best possible trading relations with EU nations.

Chloe Westley, a spokeswoman for Change Britain, responded to the criticism saying its research showed the £450m was “just the beginning”.

“There is a world of opportunity out there for us once we take back control,” she said. “Doomsayers like Tim Farron are not being straight with the British people. Staying in the EU’s single market and customs union means we cannot control our laws, borders, money and trade. Instead of trying to block the will of the people they should help us build a brighter future for Britain outside the EU.”