Institute for Fiscal Studies (IFS) director Paul Johnson says the dividend doesn't exist as the United Kingdom faces a steep exit bill, much of the money that would have gone to the European Union has already been promised elsewhere, and the Office for Budget Responsibility has calculated public finances will be £15 billion a year worse off due to Brexit.
The Prime Minister's claim that a "Brexit dividend" will help fund the 3.4% increase in spending was widely attacked as unrealistic - even by some Conservatives.
The NHS has been struggling to cope with funding shortages in recent years, particularly during the flu-ridden winter months.
The figure tops the controversial £350 million a week increase promised by the Leave campaign during the referendum.
"We're going to ensure there's a 10-year plan for the NHS", she said, with more doctors, more nurses, and "significantly more money" invested in the service.
The Prime Minister has said the NHS is to be given a "birthday present" of an extra £20 billion a year in funding annually by 2023, and argued technology must be a crucial part of driving productivity improvements over the next decade.
Ahead of a major speech on the issue on Monday, Mrs May added: "As a country, we need to contribute a bit more in a fair and balanced way".
NHS England chief executive Simon Stevens welcomed the money, saying "it represents a clear gear change in the amount of funding that will be available for the next five years, compared to what we have had over the last five years". "And we want to listen to people about how we do that, and the chancellor will bring forward the full set of proposals before the spending review".
The move comes as Mrs May faces another turbulent week in Parliament on the Brexit front with Tory rebels again threatening to defy her over how much influence MPs will have over any withdrawal deal.
She said she wanted to see better mental health services and cancer survival rates.
With dubious sources for funding and a deficient investment from the start, Theresa May's plans resemble more and more "a sticking plaster" than a real solution to the NHS' growing ailments.
"The important point is that you can only afford to fund the NHS well if you have a strong vibrant and dynamic economy where the government is focused on enterprise and growth, so that's why I think we're able to do it", he told reporters in Geneva.
The government hasn't confirmed how the budget increase is to be funded, but speaking to BBC Breakfast, health secretary Jeremy Hunt said more information would be announced in the budget. "She won't stand up to vested interests and is instead asking patients to rely on a hypothetical Brexit dividend".
"We also remain concerned about the fate of social care".