Sorry you have had no luck. We have a lot of allotments near us, but most of them do not allow livestock nowadays, and there is such a waiting list anyway. There must be someone near you, who has perhaps given up keeping hens, but still has their plot.
There again, just lately I have seen a few small "allotments" round here, or crofts of around a third of an acre, priced at £30,000!!!!
My house and field are still empty, and funny enough no one has approached me to ask to use the land - which would be ideal for poultry/goats etc.