It's best to start looking for student accommodation in Southampton (https://www.graddinghomes.com/uk/southampton) as early as possible, ideally around January to March for the next academic year. University halls tend to fill up quickly, so applying as soon as applications open is recommended. Private rentals and shared student houses start getting listed around spring, so securing a place early will give you more options and better deals
I agree – finding student accommodation in Southampton as early as possible will save you money and give you more options, especially as halls of residence Retro Bowl (https://retrobowlplus.com/) and private rentals tend to fill up very quickly!