I suppose these things come better form the horses mouth so to speak.
Shep Woolley has written, does write songs and stories of the 20th century Royal Navy.
He is probably not as famous in the folk world as Cyril Tawney or Tom lewis, because initially his songs were aimed - at RN sailors and RN life - more than some 'civvy' idea of what the navy is about.
There aren't many - rolling tideways,setting suns or yo ho ho's - but there are tales of being - not happy with the situation on board ship 'Tiffys getting more free time - hence working from a bed'
Radar plotters (RP's) who spend their time on watch in an air conditioned operations room - away from the wind and rain and yet still manage to get the ship lost.
The criterion was a pub in Commercial road in Portsmouth - frequented by prostitutes (of both sexes) tranvestites, Rough tough women who would often fight eachother and the sailors - The reference in the Vernon verse of Roll on me time to 'Heard the bell ring' - means its had its time - the bell has rung - it had been listed to be closed
down -
Nothing to 'ping' The explanation - Pinging in naval official terms
refers to the sonar return contact which makes a 'ping sound'
but Pinging in this song has a double meaning - for when a sailor is ashore -if he pings someone or something he 'homes in' be it a fanciful female, or an item in a shop window -
The Criterion being famous for its clientelle as explained above - Sailors with little or no money on a night out (run ashore) would spend time in the bar allowing the old gays & rough old gals to chat em up and buy them drinks - in the hopes of 'fun later'   
when closing time came, the sailors went to the toilet (heads) and left by the back door /rear entrance ( not too good a choice of words)
and returned onboard or to another club, the chatter upper would be left waiting in the bar for their return and be dissapointed - (they had been pinged)
sailors liked to be reminded of such antics - hence the popularity - but a song is what you make it or you read into it - so the secret is Sing it... but don't dig too deep into what its about if you are easily offended.
sw