If you don't want the hassle/timings of the coach then you can make it easier/cheaper by doing:-
Drive to Dunwich on Saturday afternoon
Leave car/van in car park
Get bike out of car and pootle to Ipswich/Darsham
Get train to London with no problems about numbers of bikes on the train
Ride to London Fields
Do Ride
Breakfast
Swim (including big fluffly towels and change of clothes in car)
Couple of hours kip in car (don't be a cock and drive when really tired)
Drive home with few travel worries
With dismantling and creative packing you can get 4 bikes in a car, plus 4 people plus stuff. A 24 hour car rental, one train ticket and petrol will probably cost about the same as 4 coach tickets but you get to the convenience of having your stuff (towels, food, change of clothes, etc) at the destination already; and you can work to your own timings. No queueing in the rain.
Of course, if you bail on the ride (mechanical or lack of HTFU spray) then you've got some logistics to solve, but no real difference to bailing on the ride anyway (it's still o'dark'thirty and you're in the middle of nowhere, instead of getting home you need to get to the car in Dunwich).
If you don't want the hassle/timings of the coach then you can make it easier/cheaper by doing:-
With dismantling and creative packing you can get 4 bikes in a car, plus 4 people plus stuff. A 24 hour car rental, one train ticket and petrol will probably cost about the same as 4 coach tickets but you get to the convenience of having your stuff (towels, food, change of clothes, etc) at the destination already; and you can work to your own timings. No queueing in the rain.
Of course, if you bail on the ride (mechanical or lack of HTFU spray) then you've got some logistics to solve, but no real difference to bailing on the ride anyway (it's still o'dark'thirty and you're in the middle of nowhere, instead of getting home you need to get to the car in Dunwich).