Agree with the points made by Adfly and Rivet Joint, extension of the runway southwards is a complete non starter. Apart from the cost of a bridge over the M27 the motorway surface from JCT 5 eastwards would need re-profiling to provide the standard 4.8 clearance for high sided vehicles. This is not possible.
Quite apart from this road issue, significant southward extension of 20 take-off distances is not possible due to multiple trees and the hill which penetrate obstacle protection surfaces. I understand that a recent survey has thrown up additional trees (little b***ers keep growing) which have resulted in additional take-off weight restrictions (around a tonne less) for the E195/E170, which I believe was a contributory factor requiring recent ALC/AGP flights routing via Bournemouth.
North is the only way to go, but again obstacles in the 20 approach area (rail yard, sheds and houses in Campbell Road) prevent extension of the current very short landing distance on 20. This again, especially with a wet runway, is performance limiting. Years back having killed off Air Europa B737-800 operations, following multiple diversions when the runway was wet.
If SOU is to prosper it needs another low cost carrier with A319/A320, something that is not going to happen until a usuable runway (both ends) in the order of 1800-1900 metres is available, and there is somewhere to park them. Unfortunately BAA's owners do not appear committed to any such investment, content to make a small annual profit and maybe wait for the next buidling boom before declaring the business no longer viable and selling off the site for non aviation development.