Southampton has various dive sites, but there's some excellent ones to the west of you in Swanage and Weymouth/Portland. Dive boats do leave from some of the marinas, but the diving's generally south of the Isle of Wight, such as
Wight Spirit who loads from Lymington.
What sort of diving do you do? If it's recreational, there's lots out of Swanage and Portland. If it's technical, south of the island is good but sensitive to weather. Again Swanage and Portland further offshore.
Dive clubs are another option. There's some BSAC clubs around which are good. Lots keep their boats in Portland.
Can recommend Swanage. Just get their early enough to park on the pier and have a great day's diving and taking in the seaside atmosphere. Classic starter wrecks from Swanage include the Kyarra which is a 15 min boat ride on the
shuttle. Nice 30m dive.
Also there's the diving lake at
Andark who are also a PADI club & trainers.
Obviously the season's at an end now as we wait for the first big storm of the season to mess up the visibility and drop the temperature. Some boats run all year round out of Portland (
Skin Deep,
Scimitar) as there's always the harbour to drop into - plenty of wrecks in there.