Historical version 2 of Harrison Clinic (view current version)
The Harrison Clinic is Oxford's main GUM clinic. They offer entirely confidential STD testing, as well as contraception and advice on sexual health. Appointments are normally required, though you should be seen within 48 hours of making one, although there are drop-in HIV tests from 1:30pm to 2:30pm.
The Harrison Clinic has moved to Blackbrid Leys and will be moving again to Cowley not long after. Probably best to check http://www.oxfordshirepct.nhs.uk/local-services/family-planning.aspx for the latest info