It wasn't "a plan" at all, but simply how the Highways Agency referred to this particularly trunk road. There have, as you point out, been plans including a Worthing bypass (f only!), something like that shown below. I think Lord Bracknell knows more.
Er, there was a double track right up until about 1990 and there is plenty of room for it. None of the track bed has been built on except in lewes, but that section doesn't matter as there is an alternative route via Hamsey.
The Lewes to Uckfield line and Eridge to T Wells branch line were both closed for different reasons, neither of which were anything to do with Beeching.
Oh and FFS.