The website is awful. It is particularly marred at times by too many biting and unnecessarily sarcastic comments, focussing on entirely the wrong things. They quite possibly need to find a competent PR person if they hope to progress further...
Leaving Brighton, trains will apparently take the East Coastway (where there are already at least 5 trains an hour I believe), until they reach Lewes. They won't actually reach Lewes, however, as that would accidentally provide connectivity and, more to the point, massively slow down journey times. Instead, they propose some expensive link thingy out towards the former Lewes-Uckfield alignment, which they propose for reopening. (Lewes-Uckfield reopening is actually the sole original point of the campaign, they've just fleshed it out into something that they reckon politicians could get their teeth into, which is as a result an unlikely to actually happen mega-project).
They then trundle along the Oxted line from Uckfield to just shy of South Croydon, where they suddenly realised there was no capacity. In an inspired move, they therefore propose opening another section of old line from just north of Sanderstead to Elmers End. This old line is used in a considerable way by Tramlink at the moment, but they propose some vague expensive solution to this issue as well, involving double deck rail formations.
From Elmers End they intend to magic up some capacity on the Hayes line up to Lewisham, which is almost fathomable, but there again they meet a sticking point in that there is no available capacity from Lewisham into London Bridge. In their original proposal they forgot to actually stop and think about this. So instead, they have now come up with a plan to tunnel from Lewisham to Stratford, forgetting that this wouldn't help capacity between London and Brighton in any way at all, would require even more duplication of services to allow travel from a variety of termini to places like Brighton, and would duplicate the DLR which already operates in this corridor.
In it's most recent incarnation, they also appear to propose a link from the the BML tracks near South Croydon to the absolutely-impossible-really-not-happening-what-are-they-on link to Elmers End, which I can't recall seeing before, although I may have done. Hence "Stanwick".
They also propose reopening the Tunbridge Wells-Eridge as a branch, which is a good idea to provide regional connectivity and thus is a part of the project they tend to overlook.
So, to summarise the awful post I've just written, Brighton-Falmer-(Lewes)-Uckfield-[Tunbridge Wells]-Oxted-Sanderstead-Elmers End-Lewisham-Canary Wharf-Stratford.