There've been quite a few threads recently on STIs and GUM clinics, so thought I'd bump this to add my experience. Hopefully knowing what to expect will encourage some that are thinking about it to go ahead and get tested.
Since asking the original question, I've now been to Whittall Street Clinic three times (which felt right for me due to my punting frequency).
How it works:
They run 3 walk in sessions per day. 9am, early afternoon and late afternoon (can't remember the times). The walk in sessions have limited slots and are in very high demand. My first attempt, I arrived an hour early and was turned away as the slots had already been taken.
You can book an appointment online. This is what I do and what I recommend doing. I usually book ~ a week in advance. The location is walking distance from the Bullring/New Street so I book for a day I know I'll be in the city centre. I have always been seen bang on time. Appointments take ~45 minutes.
You fill in a form on a touchscreen computer in a private kiosk, and this determines who you see first, nurse or doctor.
If you have no symptoms, you'll see a nurse. You'll be asked a few questions, have a blood sample taken and give a urine sample. They also do instant (but not 100% accurate) HIV and syphillis tests, which involve a small amount of blood taken from your finger. If you want to speak to a doctor, you can do.
All the details you provide can be fake except for a way for them to contact you with results. I have given a fake name and dob. They don't need a door number, so I have given my real postcode. And my real mobile number- those with partners who check their phones may want to use their punting number as they do text you appointment reminders and the result, something like 'Your test results on -date- for HIV, gonorrhea, chlamydia and syphillis were all normal'.