I almost took out private health insurance, 3 years ago, for me and my family. The terms of the insurance were quite complicated and in the end I decided not to bother. Like you, my main worry was cancer, although i was more concerned for DH as his dad died from it quite young.
I was then diagnosed with breast cancer last August (no family history) and could have kicked myself for not taking out the policy. I've now just finished my treatment (mastectomy/chemo/radio) and I'm not sure, with hindsight, whether i would have bothered getting cover.
My neighbour was diagnosed 3 years prior to me; she had private insurance and we had exactly the same surgeon and same treatment, within the same timescale, at the same hospital. The only difference was that, when she went for chemo, she wad taken through to the pricate side of the hospital which is more plush; she didn't have to wait around for treament ( id be waiting for up to two hours); she had a bed to lie on, I had a reclining chair; she had a nice prawn salad on a plate, I had a packet of sandwiches. When she had consultations with her oncologist (who also works for the nhs) she'd be in a nicer room and probably given a bit more time to mull things over with him.
The disadvantage of being a private cancer patient, however, is that you have your one consultant/ oncologist, rather than a team. As an NHS patient, your oncologist has a weekly meeting with other specialists to discuss your case, this doesn't happen with the private specialist.
I did pay for a one off consultation with a private oncologist at a different hospital, just to get a second opinion. This cost about 200 quid.
The only reason I'd consider private insurance now would be for the extra drugs that are sometimes available for private patients that haven't been approved for the nhs. You can take out an insurance policy just to cover this though, without all the frilly extras and that is something that I would have done, with the benefit of hindsight. Although, so far, this hasn't affected me in any way, it could at some point in the future.
I think it boils down to how much soare cash you have. Private insurance would have cost us about £100 a month and that's a lot of our family money. If we were a lot wealthier then it might have been worth it. Having cancer is shit and treatment isn't nice so I would have appreciated those little extras but, on balance, they aren't worth 100 pounds a month from our family pot.
Whatever you decide, check the details because it's so complicated .