The British Biology Olympiad is administered as an exam. Therefore, only your teacher can register candidates, and invigilate them. If you want to take part you must convince your teacher to make the arrangements!
You could politely and kindly explain that the competitions are free, sign-up is simple, the vast majority of participating schools receive at least one medal, and that invigilation could be as simple as watching you during a lunch-break.
All contact between UKBC and students should be made via teachers (except for in-person events such as the IBO).