The nice ladies in Ipswich told us that Greater Anglia have ordered new trains without a dedicated carriage for bikes, that could get messy.
One option for those with a car/van:-
Drive out to Dunwich on Saturday morning.
Leave car there.
Get train back to London Saturday afternoon (with bike if you've not left it in London).
Ride Dunwich Dynamo (with added incentive that car is at the far end).
Arrive at beach with car nearby containing supplies, towels, food, drink, etc.
Have a doze and drive back home with no train hassles.
(The only time I've done DD I cycled back to London so I've never had to worry about transport issues apart from my own legs/willpower.)