Mike, I'd the same as a student when visiting the Old Bailey. A court official was most concerned that I might be writing down the evidence, which was forbidden. I showed him that my notes were all about legal procedure and court room practice, not evidence, and he let me continue.
The only good reason I can think of is that people might record verbatim what witnesses in court said, for the purpose of informing witnesses waiting outside , so those witnesses could alter their story to fit .