If you’re taking the amateur radio exam either in person, or online, photo ID is required by the RSGB.
The reason that RSGB require a photo ID, is to prove that the person sitting the exam is the named person.
If you don’t have a passport or driving licence, any other photo ID will do, even an expired one.
As you’re probably aware, you now need photo ID to vote, see apply for voter photo ID.
If you really have no photo ID, give the RSGB exam team a call on 01234 832 700 to see what they recommend.