Big British Gas call centre in Central Southampton is always recruiting. As is The Royal Bank of Scotland one, which is also fairly Central. I belive both recriut through local agencies (Blue Arrow I think).
The Mortage Service (TMS) are by Soton Airport or there is B&Q's Call Centre in Fareham as are Telsis. DO not know why you want to move down there, been made redundant by a company in Fareham and have no intention of returning to Hants.