The song is "Diamond Lilly," "Tiger Lilly" or "The Finest Fucking Family in the Land". The tune universally(?) used is "The Road to the Isles". The UNCENSORED song is sung with a false Cockney accent (e.g. dropping "h"'s) by Oscar Brand on his "X" LP.

The song goes back to WWII according to Les Cleveland's 1959 book _The Songs We Sang_. Les can be heard sing the song here:

http://www.immortalia.com/mp3s/field-work/patrick-collection/les-cleveland/03%20-%20Tiger%20Lily%20%5BAka%20The%20Finest%20Fucking%20Family%5D.mp3

I have spent time accessing the relation the of "Finest Family" with "Life Presents a Dismal Picture" which is sometime sung to Deutland Uber Alles.