The thing is you need to get away from the mindset that the low cost carriers revolve around the UK. Both companies mentioned in your message have a larger European presence than that in the UK so why would they necessarily be too concerned about expansion at Southampton? The airport is reasonably untried regarding daily flights using equipment as large as an A319 or a B737 let alone putting 4 of them in there and with LGW not far away why would easy even consider the risk? What SOU management want in regards to the LCCs being based there is irrelevant, what is relevant is whether these airlines want to base themselves there. Time will tell.