The story is set in the modern day real world, and the character in question is English, male, born in London, 41-years-old and now working for the military.
I've tried searching "unique british/english nicknames" on Google but all I get are either lists of uncommon first names, or lists with nicknames (like this one http://www.britishbabynames.com/blog/uncommon-and-unusual/) we absolutely do use in the US (like "Nico" for Nicolas, "Alfie" for Alfred, etc.) I've also tried looking for derivations of Baz/etc. but that has given me only more of the same, like Bazza/Mazzer/etc.
Thanks in advance.