Which seaside town?

Not Southampton, though that is where Michael Murray's ship had docked. The city has never offered the sorts of "seaside" facilities featured in TWIQ. A couple of script references reveal that Murray had travelled from Southampton by train for a day out.

There were/are convenient train services from Southampton to Brighton, Bournemouth, Southsea, Bognor Regis and Worthing, but of course any one of a number of seaside resorts could have "stood in" for one of these. Possibly the scenes were filmed in Brighton, the most convenient of the resorts I've named for the crew and cast to travel to from London?