I think that is the nub of it. You may have a right to keep chickens, but going at it bull headed and ignoring the niceties are going to get you nowhere.
Where I am they would say move to one of the sites that allow them, then comply with all our provisions of how your set-up will be and if not we can wave nuisance or other problems at you till you quit or we end your tenancy. I am sure they would happily shop me to DEFRA as well if they thought I was flouting their rules on registration or bird flu prevention.
I don’t think Snailsbane site is being difficult at all. Ask permission and you will likely get it. John’s piece offers a lot of useful advice about getting people including plot neighbours on side. That is going to be needed, because complaints of smell, rats, noise or other nuisance will likely mean you are told you can no longer keep chickens there.
Sometimes getting what you want is a bit more subtle than waving a law in people’s faces and demanding your rights