A pressure group backed by a string of former Vote Leave campaigners from Michael Gove to Gisela Stuart has claimed that exiting the EU with a “clean Brexit” could save the country £450m a week.

During the referendum campaign, Vote Leave controversially argued that leaving the EU would leave an extra £350m a week to spend on the NHS.

But research from Change Britain goes a step further by arguing that a complete break with the EU could be even more beneficial.

The group includes some former remain supporters but its founding members are largely made up of those involved in the Brexit campaign, including Tory former chancellor Nigel Lawson, Tory donor Peter Cruddas, Digby Jones, who is a former head of the CBI, and David Owen, the former Labour foreign secretary who went on to help found the Social Democratic Party (SDP). Boris Johnson, the foreign secretary and leading figure in Vote Leave, recorded a video supporting the group’s launch, although he is not formally affiliated.

Its research suggests many of those linked to the Vote Leave group 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 Britain’s rebate, the possible budgetary costs of leaving and the lack of any indication that this cash will go to the NHS.

The report from Change Britain claims the UK economy could benefit by £24bn a year by leaving the single market and customs union, calling this scenario a “clean Brexit”.

It argues that in a likely outcome this would deliver annual savings of £10.4bn from contributions to the EU budget and £1.2bn from scrapping “burdensome regulations” while allowing the UK to forge new trade deals worth £12.3bn.

The cabinet is split over the issue of how to approach Brexit, with some of the most hardline members such as Liam Fox, the trade secretary, keen to leave the customs union, while others such as Philip Hammond, the chancellor, are pushing 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 wants the best possible trading relations with EU nations.

Groups pushing for the UK to stay in the single market, such as Open Britain, backed by Lib Dem former deputy prime minister Nick Clegg and former Labour leader Ed Miliband, argue that a “hard Brexit” would be damaging to the economy because of the risk of tariff and non-tariff trading barriers.

But Change Britain claimed its estimate was “very conservative” and that the benefits of withdrawal from the single market and customs union could be as much as £38.6bn a year.

Even the lowest forecast within its range of likely outcomes was a boost of £20bn, although the figure does not appear to factor in the possibility of large-scale loss of exports to the remaining 27 EU nations, which advocates of a “soft Brexit” argue could happen in the worst-case scenario.

Britain exported around £220bn of goods and services to the EU in 2015, while imports from the EU totalled around £290bn.

Change Britain said that the biggest prize on offer was in potential trade agreements outside the EU which Britain could strike if it left the customs union, which requires it to take part only in deals negotiated by the European Commission.

Depending on how many deals the UK secures, GDP could be boosted by between £8.5bn and £19.8bn, Change Britain claimed. The lobby group said the single market would allow Britain to scrap 59 of the 100 most burdensome regulations on business, potentially saving more than £4bn in the highest estimate.

However, the group has estimated likely savings at only around £1.2bn as the government has pledged to transfer all EU laws into UK law and particularly to preserve protections for workers.

It also said that the government’s promise to continue with subsidies for farmers and other industries means that the total saving from ending contributions to Brussels budgets will be around £10.4bn, rather than the £14.7bn which the UK currently pays.

The research coincides with comments from Mervyn King, the former governor of the Bank of England, who told the BBC on Monday that Britain may be better off going for a hard Brexit that would mean leaving the single market and customs union.

Lord King, who has been more optimistic about leaving the EU than many economic commentators, acknowledged that Brexit would bring great political difficulties and would not be a “bed of roses”. But he also said there would be many opportunities economically for the UK striking out on its own.

The crossbench peer, who led the bank for a decade until 2013, said the UK should leave the European single market and warned there were “real question marks” over whether it should seek to remain in the customs union, which would limit its ability to forge trade deals on its own.

