I'm sorry to have to disagree with @BeGentlePeeps
Maybe there is a huge regional variation, but our experience of cancer diagnosis and treatment was very different.
My DH was already scheduled for his op (privately) while waiting for an NHS referral for a scan!
The dr who suspected cancer advised him to allow the NHS referral to run but at the same time pursue the private option and see which happened fastest.
We did our homework and chose one of the top surgeons in the UK, he had his major op quickly, and the results of the biopsy within under a week.
From first suspicion of something wrong (and this was initiated by us, using private cover) to the operation itself, was around 4 weeks. The NHS hadn't even provided an appt with a specialist in that time.
He was then scanned every 4 months for a long time, far more than the NHS allocation of post-surgery scanning. The scan results were sent to his dr within an hour, to discuss. In the NHS some people, we hear, are waiting weeks for scan results.
He was also eligible with private cover for licensed drugs which were not (yet) agreed by Nice.
I agree that once you are in the system, you often get good treatment, but it's the delays that are the factor and also access to treatments.