There are regular youth championships in the UK. This and more information about activities for young go players you can find at the British Go Association's youth page.
From the comfort of your own home, you can play Go online with other people from all over the world. How does it work? Simple - Go to the KGS-Go-Server website. From there you can create an account and download the KGS program (CGoban) onto your computer.
Know of any other events (live or online) for kids in the UK? If so, let us know with an email, and we'll add them here!