During the 2016 referendum campaign on European Union membership, the pro-Brexit camp claimed that Britain was sending 350 million pounds a week to the European Union and should spend that money on the NHS instead.
Asked about the scepticism over the Brexit dividend - official forecasts are that departing the European Union will cost the public purse around £15bn a year, while much of the European Union contribution has already been allocated for the next few years - May insisted it existed.
"What is becoming increasingly clear on both sides of the border is the Tories and the SNP only care about headline-grabbing figures and sticking plaster solutions, rather than a plan to fix the health service for the long term".
"It must be a plan that tackles wastes, reduces bureaucracy, and eliminates unacceptable variation, with all these efficiency savings reinvested back into patient care".
The NHS marks its 70th anniversary this year.
May admitted the "Brexit dividend" would not be enough to generate all the extra health service funds. They say they're going to increase borrowing but they haven't said by how much, and they haven't told us what the effect will be.
In 2002, then Chancellor Gordon Brown announced a 1 percent hike in national insurance contributions, a payroll levy, to help finance a 6.1 billion-pound increase in health spending and it was a popular policy.
The OBR, government backed organisaton, and the Institute for Fiscal Studies, their analysis says that actually there will be a Brexit cost, there will be no dividend.
"I want to make sure that as see as we see this £2 billion in additional money coming to Scotland that those who work in our health service, who have been telling us that they need this key investment, will see this money coming through".
On the question of raising income tax to help finance extra funds for the NHS budget, May was not able to explicitly say who would bear the brunt of these increases.
"Labour would have invested almost £9 billion extra this year in the NHS and social care, while asking the wealthiest and big corporations to pay their fair share of tax".
Historically, every year since the NHS was created, the amount of money it receives over the top of inflation has increased by 3.7%.
Downing Street had earlier said May would deliver a speech about the NHS on Monday, giving no further details. This is unsustainable and we call on the Prime Minister to specifically address this in the detail of her plans, ' she said.
Shadow chancellor John McDonnell told BBC Radio 4's Today programme: "We need to have confidence in what's being said".
The government has yet to confirm a plan for finding up to £11bn of the money promised yesterday, with the PM telling Swarbrick that tax rises are on the way in the autumn budget.