That’s an interesting question, the answer is “it depends”. 
As far as the NHS is concerned, there’s a postcode lottery for speed of diagnosis. 
At its best, your local NHS hospital will match going private. At its worst you’ll be waiting far longer.
Referral to treatment ought to be within 62 days for most cancers in England. 
New treatments are not generally immediately available on the NHS because an organisation called NICE needs to study how cost effective each treatment is. For example a treatment which costs £1m per patient but adds only an average of 10 days to life expectancy wouldn’t get through. This is similar to the USA where medical insurers undertake a similar process. 

That said, many novel treatments (many funded by CRUK) are available as part of clinical trials.

Finally, all treatments are free at the point of care for UK citizens. No-one in the UK is made bankrupt by the direct cost of cancer care. 

I hope this helps!

Dave

Hi

Depends on the type of cancer you have, and what grade, stage etc, as stated by @SFUC.  I live in Derbyshire and had Stage 2, Grade 3 breast cancer and was diagnosed in August 2023.  Treatment started in October 2023 (but in between were lots of appointments with consultants and specialist nurses).  I did have immunotherapy in the form of Pembrolizumab alongside Carboplatin and Docetaxel chemotherapy, followed by EC2/Pembro combined.  The treatment was successful and I had a lumpectomy in April 2024.  However, the immunotherapy has caused issues with my kidneys, reducing the function at one point from 76% to 19%.  With treatment and hospitalisation, it is now up to 56% but they don't think it will ever return to my previous 76% baseline.  So yes, the NHS are offering new immunotherapy, targeted treatment, but it is on a case by case basis.  Not everyone gets it and likely depends on the type of cancer and treatability etc.  It is also not a miracle drug, as it clearly comes with its own complications along with the possible benefits.   

Your question is a little difficult to answer in detail, as it is a bit vague. But I hope my "case study" helps provide you with some information.

Best wishes and good luck.