private medical insurance won’t help that much without private infrastructure and systems though.
In Australia the hybrid private/public system is facilitated by government funding the private services.
The public hospitals are the same as the NHS, free ED, inpatients, outpatients, therapy and outpatient mental health.
private insurance only gives access to inpatient admissions to private hospitals - you still need to pay to see private therapists (occupational therapy, speech, physio, psychology etc) and private clinicians including GPs. There are also private labs and radiology providers.
The government pays for all of these services through Medicare, a provider can charge on top of this and the patient will pay the “gap.” I took my daughter to a private dermatologist for her acne (now gone!), I can’t remember the fee but was 320ish, of which I paid about 170 dollars. Follow ups are much cheaper and also subsidised.
Some GPs will bulk bill, ie just be paid the government amount so there is no gap to the patient. Most private lab tests are bill billed, most imaging, but not all.
You pay a part cost for prescriptions, cheaper if you have a chronic condition or are low income. The governments subsidises the cost of the medications and you pay the same gap, irrespective of whether it was prescribed by a GP, private specialist or through the hospital.
I don’t think any of this would be acceptable to people in the UK though, because there are some costs.
i have recently tried to illustrate how well it can work by giving the example of a 7 year old boy with ASD/ADHD/gross motor delay and Anxiety.
He could see a public paed (no cost), bulk billing GP (no cost), have private blood tests looking for nutritional deficiencies due to picky diet (no cost), private X-rays when GP suspected a fracture (no cost) and go to public ED with a chest infection (no cost).
Fortnightly OT, physio, psychology and speech are paid for by the government though the National Disability Insurance Scheme, due to his disorders (no cost)
The parents would have to pay for his long acting stimulant medications, with the cost down to, say, 8 Australian dollars because his meds are subsidised because of his disorder and/or his parents are low income.
I’ve posted this before on MN and a typical response is, “I can’t believe you have to pay the equivalent of a few pounds a month for medications. I’ll stick to our wonderful NHS, thanks”.
There will be no appetite, I think, for an accessible private system unless the public accepts that everything won’t be “free”.