I applied to Central last year through UCAS on deferred entry, but for their "Drama, Applied Theatre and Education" course.
I have never joined a Drama club outside of school but I was heavily involved in drama in my school - directing school plays, starring in school plays, being the Chairman of the Student Drama society, performing in a Physical Comedy show that toured San Francisco, teaching and directing a class of Year 9 students, leading workshops with exchange students from France, Germany, Japan... the list goes on! Ha ha. It's a wonder I had time to fit in my school work!!
But I never recieved outside of school "training" or went to a Drama school before applying to Drama School. As long as you can show you have a real interest, have experience (even if it is in school) and have a natural flair for all things theatrical - everything else becomes irrevalent.
I can't remember who I heard this off... but I think LAMDA see it almost as an advantage if you haven't had any formal training, as it means you are a blank canvas, so to speak, so they can mould you however they want. Many of the "elite" acting clubs/training for kids seem to just produce clones, who all act in the same way, with the same voice and the same notion of what is "good acting."
I don't know if I'm making sense, but I guess what I'm trying to say is...
Don't be put off if you've had no formal training. Just be confident in yourself and in your abilities and that's all the Drama School want to see.