Don't know about Southampton itself, but avoid the Fryern Dental Practice in Chandler's Ford – dentist is all right but the receptionists were dreadful. Got a letter from them saying I owed them £20 for missing an appointment that was for the following week!
If you can get to Winchester the Parchment Street Practice is excellent – really nice people, nice premises and incredibly accommodating. Private, but you get what you pay for, and to be honest I don't think they are any more expensive than going NHS – they certainly don't sell you anything more expensive than you need, and don't force you to go for a check-up every six months to stay on their books.