EVO,
if you want to experience Southampton environment, the best way is probably just to do it FROM Goodwood, after all it is not far by air and you will know both your aircraft and your instructor (and your instructor will know YOUR ability), rather than trying to get used to a new schools way of doing things. A good time to fit this in is the cross country phase of the sylabus, have a word with your instructor. Probably can be fitted in earlier if you want to.