there is an email address for information you can try, re Clarence and WW2 information modpersonnelaccessteam@nationalarchives.gov.uk

I found his fathers service details as well on national archives site, he also joined as a boy and ended up as a petty officer.
You need to register on National Archives site to access records, but there is no charge to download what there is for Edward Albert Egan Lewis, the father, service no 211235 He was on a lot of ships!!

Looks as if there were other children born after 1911, Ida 1912, Gordon 1916 Derek 1918 and Robert 1924 so you should be able to find them on 1939 register if they survived till then.

Good Luck