I know ... I had a brain fart mixing up Westminster and Winchester! Pay no attention to the newbie behind the curtain.
And it was Winchester Cathedral bringing people down because it stood and watched as their baby left town ,,, obviously not Jane Austen.
Still, Salisbury is a good place for a day trip relative to Southampton, and it also has a lovely cathedral. And I also like the suggestion for the Isle of Wight if it's not too dear.