There's loads of reasons to dislike NHS care and it's genuinely weird that people who are so against the NHS never manage to hit on something real, and instead resort to stuff that's simply fiction.
NHS England spends billions commissioning care from private providers. That's why we have Priory Group, Cygnet, Operose, etc etc all providing care. (And in the case of cygnet and priory, often poor quality care).
And patients have a right to chose where to get their care - that's what chose and book is.
People who don't understand the NHS think it's a single organisation -which is what you've done here- and that's not correct. Patients have a choice of where they get elective care. NHS England commissions specialist services, and 42 ICSs commission the bulk of regular services. They're not allowed by law to have a preference for NHS providers, so if a private provider can do it for the money they should put a bid in. That commissioned care is provided by about 200 - 220 NHS trusts. NHS Trusts include ambo services, acute hospitals, community hospitals, mental health care, and community care. These NHS trusts are independent organisations that have their own boards of directors and their own accounts and they can compete against each other to provide services to particular regions. This does not include primary care which is provided by GP surgeries.