Looking at the proximity of the railhead to the ferry terminal on this picture, (the blue posts on the picture are where the ferry docks), I am surprised that the port hasn't installed a crane here to detrain unaccompanied containers from the train to be loaded on to the ferry. Was this ever considered - and if so, what were the reasons it was discounted?
1. Newhaven Port isn't able to handle a big enough ship to make it economic
2. The line from Earlswood just South of Redhill to Newhaven isn't big enough for containers. It's only W6a gauge, and containers need W8 (with well wagons) or W10.
Point 1. is complicated to resolve because Newhaven's road access is limited, and not every container is going to go by train so it's not economic to invest in a container berth without a much wider regional road & rail upgrade. Newhaven also isn't in a great position for distributing goods nationally, or even up to London.
Point 2. is straightforward as a concept to solve, but would be astronomically expensive (as in would cost as much as a moon mission) and phenomenally disruptive to the Core London-Brighton line.