According to BBC political correspondent Ben Wright, Vote Leave has no power to make public spending promises – but is trying to reassure recipients of EU money their funding would be safe, he added.
The letter also said the "official bill" for the UK's EU membership was over £350m a week. Vote Leave's use of the £350m figure has been criticized by the UK Statistics Authority and the Institute for Fiscal Studies as "potentially misleading", as it does not include the UK's rebate.
But in the letter, Vote Leave said the UK had no control of the money and "could not count" on its rebate. It has previously called for an extra £100m a week to be spent on the NHS if the UK leaves.
Britain Stronger in Europe dismissed the analysis and said the Leave campaign had made 24 spending commitments totalling over £113bn, eclipsing the claimed saving made from leaving the EU.
Remain campaigner and former chancellor Alistair Darling said "just about every economic expert" had said leaving the EU would "wreck" the UK economy.
He added: "The Institute for Fiscal Studies has said leaving would lead to a £40bn black hole in the public finances, and nine out of 10 economists say leaving would damage the economy.
The UK votes on whether to remain in the EU or to leave on 23 June.
In other developments:
- Labour leader Jeremy Corbyn is to issue a call the “whole Labour movement” to campaign to keep the UK in the EU, warning jobs and workers' rights could be threatened by a Leave vote
- Leaders of some of the country's biggest trade unions have signed a letter saying they are worried leaving the EU will be "a disaster for working people"
- The Leave campaign has accused EU officials of spending taxpayers' money on "outrageous and excessive" expenses
- The Sun newspaper has backed a vote to leave, urging its readers to "set ourselves free from dictatorial Brussels". A Stronger In source said this "surprises absolutely no-one who has even glanced at the paper recently".
