And more than 24,000 people had to wait more than 12 hours in A&E departments in England in April after the decision was taken to admit them.
The figure for trolley waits is the highest since records dating back more than a decade.
Ministers have pledged to overhaul the NHS, with reforms to ensure that record spending is used in the most efficient way.
A National Insurance hike was introduced last month despite a backlash from some Tory MPs, who said the decision to break a manifesto pledge not to raise major taxes was “fundamentally un-Conservative”.
MPs expressed alarm that the reforms include the creation of 42 new roles, on salaries of up to £270,000 each, raising fears that the extra cash will be swallowed by management salaries.
It came after new research revealed one in five workers will be paying higher or top-rate tax by the next general election.
An analysis by pensions consultancy Lane Clark & Peacock found the numbers paying higher rates by 2024 will be double the total when the Conservatives came to power in 2010.
Calls for closer look at specialised commissioning
The Policy Exchange report calls for particular scrutiny of specialised commissioning, which has seen its budget rise by 50 per cent in eight years after such services were put under central control.
Mr Ede said: “The decision has already been taken to go ahead with a major reorganisation of the NHS as we emerge from the pandemic. We’ve got a real opportunity here to look at how we can get more for our money, better care and greater patient satisfaction if we think seriously about a different way of doing specialised commissioning.
“The budget for this part of the NHS has grown quickly but largely evaded political scrutiny. This contrasts to general practice and community nursing which have seen their share of the NHS budget shrink despite ongoing pressures,” he said.
The report says: “Both Department of Health and Social Care and NHS England should commit to undertaking a review of their workforce, with the intention to reduce headcount at the centre.”
It calls for greater alignment of the two bodies, “to streamline the policies, strategies, and guidance from the centre” including a merger of policy teams.
NHS England was established in 2013 as an arm’s length body from Government following reforms of the health service.
But in recent years, ministers have sought to strip the body of its independence, introducing legal changes to make it more accountable to the Government.
The report warns that amid all the changes, too little attention has been paid to the running of “specialised services” – which include chemotherapy and kidney dialysis.
Such services are currently commissioned nationally, with the budget swelling from £13 billion to £20 billion in the last eight years – more than the entire budget for the police.
‘National standards must protect against postcode lottery’
The thinktank said NHS plans to delegate responsibility for many of the services to local teams were welcome.
But it called for the creation of national standards to protect against a postcode lottery in what is provided in different areas. The report also calls for far more transparency over the costs charged to commissioners, in order to protect taxpayer spending.
Patricia Marquis, director for England at the Royal College of Nursing, said: “Ministers need to urgently show a commitment to building the nursing workforce and reduce their continuing disproportionate reliance on staff from overseas.
“This has to start by giving staff a proper pay rise and delivering a funded workforce plan to reduce the tens of thousands of nursing vacancies which show no sign of declining and prevent even more experienced staff leaving the profession.”
A spokesman for the Department of Health and Social Care said: “We needed to attract, recruit and retain highly skilled staff to respond to the unprecedented demands of the pandemic – this enabled us to build a testing system from scratch and deliver a world-leading vaccine programme that has saved countless lives.
“We are committed to delivering value for money for the taxpayer and operating as efficiently as possible.
“There are record numbers of nurses working in the NHS and we are over halfway towards meeting our commitment to recruiting 50,000 extra nurses by 2024.”