I am assuming that you go to/went to school in London? It's interesting because I believe that you have to be at least 80 miles away from any sort of professional production. I will use Les Miserables as an example.
Let's assume for a moment that I lived in a major city in America that isn't New York. If I were part of an amateur theatre group performing the show, and the national equity tour was rolling into town, it would be the job of the director to figure out when they are going to be there and when we are going to do the show. The main reason why they are against people doing non professional productions when there are professional productions nearby is due to the fact that they feel that if both productions are running at the same time. Some people would rather see the non professional production due to the fact that it is the same show and would cost them less.
Hell, I remember when my school fought to get the rights to do The Elephant Man. My high school director wanted it to be the play that they were doing. However, it was currently on the last legs of its first Broadway revival. My director made the argument that he should be allowed to have his cast do the play because of the fact that they would be starting rehearsals after their announced closing date. The group that was licensing out the play was incorrect in saying that the two were going to overlap. Now, maybe if they were going to be performed at the same time my director would have seen where they were coming from. However, the Broadway production announced its closing and they were going to be long closed when my high school would be doing it.
It ended up that the playwright heard of what was going on and gave them the rights for free. He said that he did this because he felt that there was no way in hell that a high school drama club could do his work justice. However, he wasn't one to stop them and said that if my high school wanted to do it then be his guest.
"If you try to shag my husband while I am still alive, I will shove the art of motorcycle maintenance up your rancid little Cu**. That's a good dear"
Tom Stoppard's Rock N Roll