Libraries are a good place to volunteer and usually they will take anyone over 13. They often have summer holiday schemes for young people.
Or how about volunteering for an adventure playground for children with disabilities. That is what my daughter will be doing this summer. I think this is one in your area http://www.elhap.org.uk/volunteer.html
Another idea is volunteering for the National trust offering historical information about their properties. This could be fun and informative for a young person who is interested in History. The N.T. give training in what to say and are usually keen to have younger people.
You could also look here on the CVS website. There are lots of volunteer opportunities https://www.redbridgecvs.net/volunteering/opportunities