BUPA is unusual in the private health care field as it's run on a not-for-profit basis and it operates its own hospitals.
However there are lots of other health insurance services, such as those run by Axa, Aviva, WPA and PruHealth.
Some people like the idea that there's a private health market in this country (running alongside the NHS) , while other don't. However it's a simple fact that people paying for private health care (whether through BUPA or any other provider) benefits the NHS, as those people are still paying for NHS care (through their taxes) but not using it, thus freeing up resources for other people.