I am in Portsmouth, near to Southampton.
British summers are unpredictable.
You have the fact it is the end of summer/early autumn time. So it SHOULD at least be sunny and moderately warm.
We have had warm weather up until November.
But being Britain, the chances of it being wet most of summer is high. So even WE do not know.
Southampton is a dump, no idea why you'd want to go there - any particular reason, or is it relatives and free accomodation?
In all seriousness, if you do go to Southampton and need a day to experience something, I must suggest getting an hour train and spending a day or half in Brighton.
Culturally, it is a brilliant and quirky little place and has a trillion more things to enjoy than Southampton - which is pretty much an out city enclosed within a wall, now mostly abandoned, and overspilled to the outskirts with a massive shopping centre. It is horrid!
Jenson drives it like he owns it; Lewis drives it like he stole it