The DUP's Simon Hamilton said the announcement was a "hugely welcome boost for our National Health Service".
Across the whole Department of Health (including other areas like public health) the Nuffield Trust has calculated that the increase will amount to around 3% a year, rather than 3.4%.
Mrs May is under fire for claiming that a spending boost worth around £20bn extra per year by 2024 will be part-paid for by a "Brexit dividend", despite economists saying that leaving the European Union will have a significant negative impact on the public finances.
May said: "Some of the extra funding I am promising today will come from using the money we will no longer spend on our annual membership subscription to the European Union after we have left".
"We will be able to explain exactly where every penny is coming from but we will do that in the Budget", he said.
She said the NHS is "this government's number one spending priority", and that in due course the government and NHS would work together to develop a 10 year plan for the service.
May will pledge to increase the NHS budget by 20 billion pounds ($26.6 billion) a year, or 384 million pounds a week, after Brexit, according to front-page reports in the Sunday Times, Sunday Telegraph and Observer, which were published late on Saturday.
It is expected tax and borrowing will rise to pay for the increase in funding.
But she added: 'It is essential that as more details of her long-term plan are announced, general practice is recognised for the vital role it plays in delivering safe, effective patient care in the community, and keeping the entire NHS sustainable'.
"But the commitment I am making goes beyond that Brexit dividend because the scale of our ambition for our NHS is greater still".
Mrs May is using her speech in London to say the NHS has a special place in British life, hailing the work of those who treated victims of the Manchester Arena attack a year ago.
"The Tory claim that the NHS can be funded by a Brexit dividend is simply not credible as the United Kingdom will be paying £40 billion to leave the EU", Ms Robison told the BBC's Good Morning Scotland.
The head of NHS England has welcomed the funding deal - but other NHS leaders and healthcare experts were unconvinced it would be enough.
The prime minister has been urged to admit where extra money for the NHS is really going to come from.
Mr Hunt dismissed findings from the Office for Budget Responsibility and Institute for Fiscal Studies that said there would be a net cost, not a dividend, from Brexit.
Labour's shadow chancellor John McDonnell said: "After eight years of Tory cuts and privatisation, the NHS and social care are in crisis". We certainly haven't seen that.
"However, we will be scrutinising the detail of this new package of funding to assess the degree to which it will make a real difference in both the short and long term to frontline patient care".
Mr Trump has long dismissed any news reports he disagrees with as "Fake News", dating back to his 2016 presidential campaign. While there may not be a "hidden message" in her jacket , Trump knew that wearing the outfit would prompt a reaction.
Pompeo told the same Cabinet meeting Kim had made a personal commitment, and added: "He has got his reputation on the line". US officials, however, have cautioned that such actions are reversible. "Personalities can change.
Some 5,200 families fled their homes this month as pro-government forces advanced up the Red Sea coast, according to the UN. More than 40 airstrikes from the Saudi-led coalition hit the airport since Tuesday morning, Houthi officials said.
Its biggest target has been China, against which President Trump this week ordered new tariffs on $200 billion worth of goods. Canada has announced it will impose retaliatory tariffs on C$16.6 billion (RM50 billion) worth of U.S. exports from July 1.
European Commission president Jean-Claude Juncker said duties imposed by the U.S. on the EU go against "all logic and history". For example, the CETA trade deal with Canada is helping spur double digit export growth in that market.
Apple says that with the new feature - which will arrive in the fall with iOS 12 - the company already exceeds this requirement. The companies announced the feature June 18 at the National Emergency Number Association (NEMA) conference in Nashville.
Sprint didn't share which firms it works with. "Verizon did the responsible thing, " Wyden said Tuesday in a statement . They allow users to obtain nearby emergency roadside assistance, for example, and are useful in preventing bank fraud.
A big OPEC deal- adding more than 1 million barrels - could cause prices to dip into the $2.60s or $2.70s this summer, he said . But in practice it would mean a much smaller boost of less than a 10th of that amount, effectively from Saudi Arabia.
But such resettlement programmes are a drop in the ocean, Grandi said, and they are at risk of drying up. Out of 40,000 places sought for refugees, the UNHCR has received pledges to host 25,000 people, he said.
PC gamers can expect hundreds of significant discounts on popular games and downloadable content throughout the weekend. More specifically, Steam users will be combating an intergalactic force that is trying to destroy all games.
House struggles to unite behind bills to stem border crisis
President Donald Trump announced Wednesday he will sign an executive order to end family separations at the U.S. -Mexico border. But the chances of the bill passing are unclear as is the case with any bill dealing with the volatile issue of immigration.
Geely's Volvo aims for more recycled plastics in new cars
This follows on from the brand's pledge to stop using single-use plastics at events and on Volvo premises from next year. At least 25 percent of the plastics used in new Volvo vehicle models from 2025 will be made from recycled materials .
Trevor Noah Reveals The Meaning In Melania Trump's Jacket
REUTERS/Kevin LamarqueFirst lady Melania Trump boards the plane as she departs Joint Base Andrews on her way to Texas on June 21. It's possible that Melania, whose focus is on children, may have helped encourage her husband to act.
Brazil vs. Costa Rica
Jesus had a quiet game against Switzerland in the 1-1 draw on Sunday and was replaced by Roberto Firmino in the second half. FIFA World Cup 2018 Live Score, Brazil vs Costa Rica Live Streaming: Neymar will start for Brazil .
Major Upsets as World Cup Advances
But before all that fun, supporters stayed back to tidy up their sections of the stadiums in videos that have gone viral. The Japanese have once again proven to the world that they are a people with a strong sense of civic duty.
PM on International Yoga Day
As awareness about the need for a healthy lifestyle increases, youngsters as well as senior citizens are keen on following yoga. Over 500 yoga lovers turned up to take part in over hour-long special yoga workout at the old Indian Embassy premises.
Melania Trump's office defends 'don't care' jacket
Last August, the media and public discussed the high-heeled shoes she wore to fly to Texas to view Hurricane Harvey destruction. She asked many questions, seeking assurances that they are being properly cared for. "It's a jacket .
World's 50 best restaurants for 2018 announced
Last year, only three of the top 50 restaurants had women at the helm, and all of them ran the kitchen alongside a man. Claiming the second and third sports were El Celler de Can Roca and Mirazur , respectively.
Bagley, Porter head list of forwards
However, with center DeAndre Jordan most likely going to leave in free agency, the Clippers are going to be stuck in mediocrity. Porter invited certain teams with picks in the lottery to examine him Friday. "And that's how I kind of view myself".