Jamie, if you are still interested, first look to get an idea of the market- has some good ways of finding a cheap policy. Then, I would use a comparison website. Or you could go direct to the insurers- big names are Bupa, Aviva, PruHealth and AXA PPP.
I currently have health insurance with Aviva but I only got it a few years ago, after my husband had trouble with waiting lists on the NHS. My premiums are quite low, because I chose Aviva's 'Speedy Diagnosis' option'- this covers me for private tests and scans but I actually get treated on the NHS. I'm not sure whether this will be suitable for you though if its aftercare you are looking for?
If you can get health insurance with work (or your partner's work?) I would definately recommend it- a massive perk! Alternatively, you could get a cash plan- this gives you money towards certain procedures and you don't have to pay as much each month.
I hope this helps