Dave,
If Southampton is no good and you can go as far as Gatwick then try:
Swissportuk.com
Menziesaviation.com
Servisair.com (also at Bristol)
or going the other way, flybe.com at Exeter do their won ground handling.
All are majors within the UK and are always on the lookout for good staff. As FDD says, the money is not fantastic but it does open the door to get you into the industry.
Good luck,
GH