Prominent Brexit campaigner Priti Patel has insisted there would be "more than enough money" to continue funding the beneficiaries of EU grants as Vote Leave's spending commitments came under scrutiny.
Ms Patel joined senior Tory colleagues including Justice Secretary Michael Gove and former London mayor Boris Johnson in committing to maintain current levels of funding in the latest policy pledge made by the Vote Leave campaign.
The move comes on top of promises to use the savings in contributions to the EU to provide £5.5 billion a year to the NHS and spend £1.7 billion abolishing VAT on household energy bills.
Remain campaigners branded the policy pledges "fantasy economics", warning that any savings would be eradicated by even a small economic downturn following a Leave vote.
Brexit campaigners acknowledge it is the Government that decides on spending commitments, rather than the Vote Leave camp, but the message signed by 13 senior Tories was designed to reassure recipients of EU funds.
Ms Patel told BBC Radio 4's Today programme: "We have been abundantly clear that there would be more than enough money to ensure that those who now get funding from the EU - including universities, scientists, farmers, regional funds - would continue to get money, while ensuring that could be spent on our priorities."
"We are giving money to the European Union and when it comes back, it comes back with controls, it comes back with us as government ministers and the British Government not being able to decide how to prioritise that money and what we can spend it on, it's the European Union that dictates how we spend that money.
"We are clearly saying that if we take back control of that money we can spend it on a range of our priorities - the ones that I have listed today but on top of that we can continue to invest in the NHS, we can scrap VAT on fuel which affects people on low incomes.
"These are the priorities that will make a significant difference to our country and the British public."
Despite a range of suggestions from Brexit campaigners about how the money that goes to the EU could be spent, Ms Patel insisted that the only official policy pledges apart from maintaining the existing grants were on funding the NHS and the VAT cut.
Although a range of economists and international bodies had forecast a major hit to the economy from Brexit, at least in the short term, Ms Patel said it was "pretty pessimistic that the Remain side keep talking down our economy".
She said: "There would be more economic growth through the opportunities that we would have to trade with new countries around the world."
But Labour In campaign chief Alan Johnson told Today: "Vote Leave say, in their latest fantasy economics, we are going to give all this money back - that money won't exist.
"It only takes a 0.6% movement in our wealth, GDP only has to be hit by just over half-a-percent to eradicate the £8 billion - not £19 billion that they were claiming - the £8 billion that is sent to Europe and distributed through farming subsidies etcetera.
"Losing our access to the biggest commercial market in the world, turning our back on something we created, is going to damage our economy. That's going to damage public finances, that's going to hit public services."
Labour former chancellor Lord (Alistair) Darling accused the Leave campaign of "fantasy economics", saying they had already committed to additional spending totalling £113 billion - more than 10 times the UK's net annual contribution to the EU.
This would come on top of the hit to public finances caused by Brexit, which the Institute for Fiscal Studies think-tank has estimated at £40 billion, he said.
Lord Darling said: "This is fantasy economics from the Leave campaign, as quitting Europe would wreck Britain's economy and mean cuts to spending on vital public services, as just about every economic expert has said.
"The Institute for Fiscal Studies has said leaving would lead to a £40 billion black hole in the public finances and nine out of 10 economists say leaving would damage the economy.
"The Leave campaign have had to abandon their key spending pledge after using misleading figures and have been caught pledging their claimed saving 10 times over. This fantasy economics shows that leaving is too big a risk to take."