Interestingly before covid-19 the Government were pushing for more decentralisation and all the work around ICS / STP was going ahead. But during pandemic there's been a move away from localism and a push towards central control. Having said that, here's why it's not "The NHS".
It's a collection of hundreds of legally separate organisations. A doctor goes to work for eg Lewisham and Greenwich NHS Trust, or for Chelsea and Westminster NHS Foundation Trust, they don't go to work for "The NHS".
In 2017 there were:
207 clinical commissioning groups,
135 acute non-specialist trusts (including 84 foundation trusts),
17 acute specialist trusts (including 16 foundation trusts),
54 mental health trusts (including 42 foundation trusts),
35 community providers (11 NHS trusts, 6 foundation trusts,
17 social enterprises and 1 limited company),
10 ambulance trusts (including 5 foundation trusts), and
7,454 GP practices.
(There have recently been a bunch of mergers because of ICS / STP work, so this list is wrong).
The largest is probably Barts Health NHS Trust, which employs about 15,000 people. The smallest is probably Weston Area Health NHS Trust which I think employs about 1,700 people.
These organisations are legally separate. They have their own board of directors. They employ their own staff.
To change this we'd have to roll-back the Lansley Reforms, and that's too hard to do even when we're not going through pandemic.