You cannot study in the UK with General Visitor or Business Visitor permission and you cannot register at LSE if you have permission as a general visitor for any kind of programme of study.
What constitutes study?
During my 2-month stay in London, I took several walk-in dance classes. Would this technically be a violation?
What about something more regular, but not accredited? A 6-week Karate course, for instance?
Do I ever need to worry about accidentally taking an illegal course or class? Or will any eligible institution know to ask for my residency/visa status before admitting me?