The main group campaigning for a British exit from the EU has a £14bn “black hole” in the savings it claims the UK would make if it voted to leave, Tory grandee Sir Nicholas Soames has said.

The former defence minister, a pro-European, has called on Vote Leave to explain its calculations or remove from all its campaign literature a “misleading statistic” that a Brexit could save Britain £350m a week.

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In one of its founding documents, Vote Leave indicated that the UK would be free to spend nearly £20bn on schools and other domestic priorities if it left the EU. Answering why the UK should leave the EU, the group said: “We stop sending £350m every week to Brussels and instead spend it on our priorities, like the NHS and science research.”

The £350m works out at £18.2bn a year – and was used to roughly equate the UK’s annual £19.23bn contributions to the EU as a condition of its membership. But Soames says this marks the UK’s gross contribution, whereas the figure dips to £9bn, according to Treasury figures, once the UK rebate and other EU grants are taken off.

In the event of a Brexit, the UK government would have to finance the equivalent of the EU grants. It would also have to pay to meet Vote Leave’s preferred option of maintaining access to the single market. This means that Britain would save just £5.29bn by leaving the EU. Soames said that this more modest saving would leave a shortfall of £13.94bn in Vote Leave’s calculations.

Facebook Twitter Pinterest Sir Nicholas Soames. Photograph: Peter Macdiarmid/Getty Images

He said: “Vote Leave should either explain or amend their claim that by leaving the European Union the UK could save £350m per week. Their figures fail to take into account important financial considerations such as the UK’s vital rebate, the need to reimburse beneficiaries of EU grants, and contributions to the EU budget that would still be required if we were to retain access to the single market.

“It now appears that Vote Leave have an annual black hole of £13.9bn in their sums. It is essential that the British public have the opportunity to make an informed decision. Everyone campaigning in this referendum, irrespective of which side they are on, has a duty to ensure they provide accurate information to the public.

“Vote Leave should either explain how they have considered all these financial factors, or if they cannot explain it, I believe they should retract this claim from all campaign literature and prevent their spokespeople from continuing to use this misleading statistic.”

The analysis cited by Soames, based on Treasury figures, says:

The UK’s gross contribution to the EU is £19.23bn.

The EU sends back £10.23bn (£4.89bn in the UK budget rebate, £4.54bn in public sector receipts and £800m in private sector receipts). This means that the UK’s net contribution to the EU is £9bn.

In the event of a UK exit from the EU, the chancellor would still have to finance the equivalent of the UK budget rebate and the EU receipts to the UK.

If the government followed the recommendation of Vote Leave, which says that Britain would negotiate access to the single market from outside the EU, it would still have to make a substantial payment to the EU. There are currently only two models to achieve this – the arrangements negotiated by Norway and Switzerland. Norway contributes per head the equivalent of 76% of the UK’s contribution to the EU while Switzerland contributes per head 38% of what Britain pays in. A contribution by the UK from outside the EU on a similar level to Switzerland would cost £3.71bn.

The combined total of what Britain would have to fund to match EU grants and the rebate (£10.23bn) plus the estimated £3.71bn costs of maintaining access to the single market would be £13.94bn. This means that Britain would save £5.29bn, rather than £19.23bn, from leaving the EU.

Vote Leave dismissed the analysis, which was put together by Britain Stronger in Europe, the main pro-EU group. A Vote Leave spokesman said: “It’s good to see that the BSE campaign are finally admitting the EU costs us billions. We send £350m to Brussels every week: enough to fund a new hospital every week of the year. But these figures are simply not credible, based on flawed assumptions that do not stand up to basic scrutiny. We’ve seen dodgy polls from the in-at-all-costs brigade, and now it’s dodgy sums.

“When we vote leave, we can take back control and decide how we spend our money – on our priorities like the NHS and scientific research.”

