The 2005 Forest Tracks album "Southampton in Song" might be a good place to start! By Jeff Henry and myself. Knife & Scissors Man (Graham Penny), The Sack of Southampton (Rob Sibthorpe), Looking Back (Roy Harrison), Poll of Itchen Ferry (anon), The Sinking of the Titanic (Stoneman), Northam's List (Barry Wake), The Woolston Ferry (Mike Sadler), The Bells of St Mary's (Furber & Adams), 4 o'clock on Thursdays (Ken Stephens), The Southampton Tragedy (anon), The Channels (Graham Penny), The Famous Itchen Ferry Song (Hooper & Henry), The Southampton Spitfire Song (King), Here in Southampton (Hooper & Henry).
There's quite a bit more too, from the pens of Barry Wake, Jeff Henry and me.