I reply not just as an enthusiast but also as a railway employee (LUL not the national network).
I spent quite a lot of time during 2024/2025 at London Bridge, and for the most part did not encounter any issues. However, there were one or two Security individuals who could be slightly more "jobsworth" than others and would regularly move people along even if you were seemingly doing no harm.
Towards my last handfuls of visits I was asked by a couple of the more reasonable staff to sign in at the Network Rail customer service desk. This is becoming more common at many large stations and is actually understandable. Rather than turning you away it means you are "accounted for" and everyone knows what you're doing. All staff are trained to be vigilant of customers who do not seem to be boarding any train, and will approach to check on your welfare and to see what you are doing - and it means you're discounted as being a security risk.
For the most part, the "high level" platforms at London Bridge you will pretty much blend into the crowds anyway. The "low level" platforms are quieter, and I often used to stand at the southern end of platforms 11/12 so I could see arrivals at the low level as well as most of what was arriving on the high level. This does mean you tend to stick out like a sore thumb (a sole figure at the "wrong" end of a busy station platform) but if you have signed in and have a ticket and permission and do not put yourself in danger or be a nuisance then all should be ok.
