Intrigued to know that photo in your box is it woodbine willy the padre who gave out ciggies to wounded troops in the front line....
There is a description of the Dulwich Defence Leage badge Phil mentions here... and the shape sounds similar. www.glamorganantiques.co.uk/capbadges.htm"The Dulwich and district Defence League.Later the 1st/12th battalion.On a shield crossed rifles with bayonets fixed.The scroll inscribed >Volunteers.Below the wreath the scroll inscribed "Defend our City".This was one of the regiments forming the Volunteer force of 1914 - 1919"There are also a few pictures of other London Regt badges.... For exampke 10th London County (Hackney Regiment) is a very similar shape (shield, crown, scroll at bottom) but unfortunately the central detail is not quite right.Milly