Geoghegan's song 'Cockles and Mussels' can be found on the British Library Collect Britain website under Victorian popular Music.
It is dated 1876 and the singer of the famous chorus is one 'Jim' not a Molly. The singer is a London Costermonger who is 'known the world over from Stepney to Bow'. The chorus runs
Fresh cockles and mussels alive, alive O!
Alive, O! alive O!
Alive, alive O! I call as I go,
Fresh cockles and mussels alive, alive O!

Geoghegan was born in Lancashire but lived a lot of his life in Sheffield. He wrote lots of songs we nowadays think of as folk songs and almost rivals the great Harry Clifton in this respect. He wrote 'Hey John Barleycorn', 'Ten Thousand Miles Away', 'I likes a drop of good beer', 'They all have a mate but me', 'Down in a Coal Mine', 'Johnny I hardly knew ye', 'Pat works on the Railway' etc etc.

Now regarding the origins of MM, if Yorkston wrote it in the 80s then obviously he was influenced by Geoghegan's song.