Well, an alternative might be to create a new branch off further down the existing line and bypass Jarvis Bronx to join the line to Uckfield further down. Either way, its gonna cost a few Diblies.
This is beginning to sound like a Johnson announcement now.
It never ceases to amaze me where you can't go by train in the SE. When I was in Leeds it felt as if you go anywhere in the UK from there, save the SE. Compare and contrast with Royal Tunbridge Wells - Hastings or London. Amazing.