A well-run allotment produces very little waste. Most weeds and crop residues can be composted. Prunings and hedge trimmings can be chipped for use as a mulch, or stacked in an out of the way corner as a habitat for beetles and millipedes.
If you take on a neglected plot you may find you have a lot of rubbish to get rid of. Allotment gardeners are great recyclers. The previous tenant on your plot may have made a greenhouse out of old window frames or a compost bin from For Sale boards, but over the years useful garden structures can become rickety eyesores.
Skips are provided on most sites 3 or 4 times a year.
For advice on composting, and bargain compost bins, look at the York Rotters site at St Nicholas Fields.