BUPA is one such company.
http://www.bupa.co.uk/individuals/health-insurance
No articles on the UK seem to even mention this extra private insurance market, used mainly as a means of jumping the queue - from their web site -
Health insurance can pay for quick diagnosis, such as MRI scans, and prompt treatment of acute illness or injury including operations and aftercare, that could be administered in a private hospital or as a private patient in a NHS hospital.
Unfortunately, there are quite a lot of problems with BUPA, one of the less well known being that their coverage in the UK is decidedly uneven. Anyone can sign on to BUPA, but if you are unlucky you might be hundreds of miles from the BUPA specialist who can help you.