Hmmmm, I have not yet tried taking my cargo bike to either of the two the local recycling centres, but the Council interweb site says:
"The following vehicles are not accepted at either recycling centres - lorries with a GVW exceeding 3.5 tonne, triple axle vehicles, twin axle trailers, horse boxes (either single or double axle), vehicles with a tail lift (except those cars, 4X4 cars, people carriers or caravanettes adapted with tail lifts for use by disabled residents), vehicles with a tipping body, large box vans (Luton type), long wheeled based vans or high top vans
Nowt about banning cycles, although from memory there is a sign on the gate telling you not to "walk in" stuff, but equally nothing to say no cycles.
I did once ask the staff there and they were laid back about it (before recent rule changes tho) however they were not sure if the rule of "need a permit- for £15- if you use a trailer with a bike."
Maybe an email to the council first, sent on to the local paper to embarrass them if they say no bikes.....
TBH, one of the main reasons I kept my (small) car when I acquired the work van (I originally planned to sell the car which would have forced me to make all non-work journeys by foot, bike, bus or rail) was because tax issues aside, even with a permit I can't take the big work van (long wheelbase hi-top) to the recycling centre, and unless I know for sure I can take a cargo bike or bike + trailer as an alternative that makes it impossible to legally dispose of some types of occasional household waste. Fact is though I could get as much on my bike + trailer or cargo bike as in my small car! I wonder if cargo bike with a sidecar would get around the trailer rule....?