As far as I see it, whilst I wish them well, I fail to see how Shoreham would work, or why there would be any demand for such a route - if it’s for its proximity to Gatwick, then by the time you’ve got a cab to the nearest station and got the stopping service to Gatwick, you might as well be on an express train from Parkway to Clapham Junction and onto Gatwick from there, surely? (Other large British airports are available)!
Useful routes from Alderney:- Cherbourg or Caen (nearest large [French] cities, with good rail links to the rest of France, also good for a day return in either direction), and - shock horror - Southampton, to increase frequencies on the route and increase competition to force prices down and make it more accessible for mainlanders and islanders alike… but then I’m no expert and could be proven completely wrong! Just my 2p worth.