Yamaha Junior Original Concert
is an event aimed at young composers performing their own work (not just keyboard). It is held in Europe, but not yet in the UK, I believe.
Sibelius sponsors a Composer of the Year competition which is very active in the pre-teen and teen areas. The Sibelius site also lists a UK competition called Strictly Composing, but I don't know whether that's a one-off or an annual event.
I'm not sure how it works in the UK, but in Japan, there are corporate contests (mostly for publicity) inviting people to send in jingles and other short pieces of music, logos, artwork etc. to advertise new products or new public schemes of one sort and another.