Thought I would put this up in case it helps anyone else who, like me, does not trust the medical establishment to keep things confidential.
The site http://www.letsgetchecked.com offers a service that can be untraceable. You buy a kit in a pharmacy, collect samples yourself, post them in and get results on-line. They need name, address, phone number, date of birth and email address, but none of them have to be real. Seems a good service and it has worked well on the couple of occasions I have used it.
Of course if I got a positive result I would make sure that people who need to know were told, but I would like to be in control of that process to ensure discretion.