Sorry I have to laugh when I see that - who in their right mind would get their laptop out and sit down on CLJs footbridge!
Not only would it be of great inconvenience to all the passengers following the flow system of the station for someone to be sitting there blocking the way, it would be greatly inconvenient, uncomfortable, and look a bit suspicious. Then the laptop would probably get stolen - after all a London Assembly report within the last two years said that CLJ was the 2nd station worst for crime out of those in zones 2-6... (in case you're interested ECR was first! Yes, rather shocked me too).
I think the wifi works on quite a bit of CLJ I've used it is the coffee shop on Platform 13.
The Southern Service is actually very good it works on all the 377/3 trains not just on the Brighton Line. Its part of the T mobile hotspot system so if you're a regular commuter its not too expensive. The quality is very good I've sucessfully streamed video via skype to another member on here throughout my commute from Littlehampton to Portsmouth.
Its certainly much better than whats was on offer on GNER- Ive not been on NXEC recently.