Hi GreenGirl, where are you moving back from? Welcome back to sunny England!
Bupa is one of the most well known insurers over here, but I would advise using a comparison website to find a policy because it can also be one of the more expensive. I used
www.activequote.com, pretty useful if you have no idea of the market.
I only got health insurance a few years ago when I left uni after I 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. This might be a good option for you to start with, because to be honest its the waiting lists that seem to be the problem over here.
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. To be honest though, if you are going to be spending money each month you may as well go for a decent level of cover- in my opinion at least!
Don't listen too much to the stories in the newspapers, they do tend to exaggerate, but in my experience getting quick scans and diagnosis can be a bit of a nightmare. If you did choose a comprehensive policy you would be treated in a private hospital as well- can be pretty plush!
Hope that helps