I'm in the same position as you with trying to get these tests done for the Facial Team. I was on the phone to my GP last week sorting out the tests and regarding the HIV and Hep B & C tests he said initially he wasn't sure he could do it at his practice. However he checked on the ordering system and he was allowed to put the order in, however he said he wouldn't be surprised if they don't process it as I'm not a high risk patient.
I plan to do the blood test in early July, so I'll find out then if it went through. I'm guessing if it doesn't go through then I'll have to pay to have it done privately somewhere.
Out of interest do you already know your blood type?
I'm trying to find my blood type out for the FT form they have and I'm having no luck. My GP can't test for it, the DIY home kit I got off the internet was inconclusive and I can't donate blood so can't find it out that way.