@Coting I’m not 100% familiar with the UK medical system, but the short answer is Yes, you can go to the doctor and describe the situation. They should be familiar with post-exposure prophylaxis, and if not, should contact someone who does know. In the USA there is a national hotline for clinicians. In the UK, I found this website that can help, but a key principle is to seek medical attention as soon as possible (i.e. within 72h).
@casheroo Yes, the drugs are readily available with a prescription. There are guidelines for their use, which are evolving. But, sex with a known HIV positive person certainly qualifies, as does sex with someone with significant risk factors (men who have sex with men, IV drug users).
Now, this doesn’t eliminate your risks of other STDs, like Hepatitis B (get vaccinated), Hepatitis A (get vaccinated), gonorrhea, chlamydia, syphilis, HPV. Your best bet is to discuss this with your doctor, get tested, and practice safe sex in the future.