People living with HIV can do most jobs in the UK. If you would like to be a surgeon, midwife, dentist or pilot, you can. Read here the story (Jan 2020) about the first pilot in the UK to talk openly about living with HIV. A person living with HIV doing these jobs, would just need to have more regular blood tests to make sure their viral load remains undetectable.
The only job a person living with HIV in the UK cannot currently do is a frontline position as a member of the armed forces. The armed forces have a duty of care to their staff, which includes making sure staff can access any medicine they may need. People who work on the frontline can go anywhere in the world for work and because of this, anybody with an ongoing medical condition that needs regular medication cannot be a frontline member of the armed forces. This is because the employers wouldn't be able the guarantee you would still have access to the medication required to keep you well.
For more information, read this article by NAT.