Theresa May and a “large number” of Cabinet ministers have rebuked Boris Johnson for briefing that the NHS should get a Brexit dividend of £100m a week.

The Prime Minister reprimanded the Foreign Secretary during an hour-long debate on the funding of the health service, telling him that discussions should remain “private”.

After several colleagues lined up to support the PM, a chastened Johnson failed to specify how much more cash he wanted, prompting Labour to declare he had “bottled” the issue and was just playing “internal party games”.

But May did hint at a fresh cash injection for the NHS, telling the Cabinet that health along with housing and education were ‘priorities’ for her Government in any spending of money freed up after the UK quits the EU.

In one of its strongest reprimands, No.10 said May had made clear how irritated she had been with widespread media reports that Johnson wanted £5bn more for the health service.

“The Prime Minister and a large number of Cabinet ministers made the point that Cabinet discussions should take place in private,” her official spokesman said.

Johnson famously declared on his Vote Leave battlebus that the NHS would get an extra £350m a week after Brexit, and his allies had briefed that he would on Tuesday demand £100m a week as part of a net figure to be shared on public services.

Yet despite his friends predicting that Johnson would dominate the discussion and demand his extra sum by next year, the No.10 spokesman said “no minister discussed any specific number in relation to the NHS”.

It is understood that while some colleagues such as Health Secretary Jeremy Hunt and Michael Gove supported calls for more money, many ministers – including Brexiteer Liam Fox – lined up before he spoke to express their annoyance that the Foreign Secretary had gone public.

Downing Street said that May had stressed during the meeting that the last Budget had already allocated an extra £6bn funding for the NHS.

“As regards the future, and how any return of the EU contribution would be spent, the Prime Minister reminded Cabinet that the government has consistently said that we will spend money on our priorities, such as housing, schools and the NHS,” the spokesman said.

“There will also be other calls upon that money but we will discuss those priorities at that time.

“As regards the NHS, the prime minister said there are a number of factors we need to consider as part of this. These are the the efficiency reviews that we set up on the budget to ensure that the taxpayer get best value for the money it spends in the NHS, ambitious work to integrate health and social care and reform the system, and the next spending review, which is due early next year.”

Shadow Health Secretary Jonathan Ashworth told HuffPost: “So, after all the huffing and puffing, after all the embarrassing, self-indulgent posturing, Boris Johnson bottled it.

“It’s now clearer than ever that only a Labour government will give the NHS the extra £5bn funding it needs.”

Earlier, Chancellor Philip Hammond – who was in Brussels at an EU finance ministers meeting and unable to attend Cabinet – issued his own slapdown.

“Mr Johnson is the Foreign Secretary,” he pointed out to reporters.

May introduced the discussion on the NHS and Hunt made the main presentation on a ‘winter update’ on the service.

Ministers were told the health service had been placed under significant pressure by the worst flu outbreak for a number of years.

In the first week of 2018 flu admissions were approaching that seen in the highest week in 2010-11, which was the time of the swine flu epidemic, but staff were doing an excellent job in treating patients, Hunt said.

“Cabinet were told the most extensive preparations ever had taken place due to enhancements to the 111 phone line, with more doctors and nurses on the end of the line,” No.10 said.

“An estimated 2.3m people have been diverted away from A&E. An extra 1m people were also given flu vaccinations.”