[Markuk]

It say on my lease (I really want chickens)
keep in or on the Premises any pigs poultry pigeons animals reptiles
or other livestock of any kind save for common domestic pets (and
then only with the prior written consent from the landlord) or a service
animal and in all cases to keep them under proper control ano not
allow them to cause nuisance, disturbance or annoyance to any other

[New shoot]

The wording you quote is pretty standard for lease agreements, so all you can do is ask for permission from your landlord and see what they say.  If you can make your case that they will not be a nuisance, they might agree. 

[johnjsdb]

The allotments act 1950 may help as it seems to say you can keep hens and rabbits provided it is not predudicial health or cause a nuisance.

[New shoot]

The allotments act 1950 may help as it seems to say you can keep hens and rabbits provided it is not predudicial health or cause a nuisance.

True and in theory I have the right to keep hens on my allotment, but the council effectively say no to that on our site and a lot of other sites around Reading. 

Some help here from an article on the main site by John

https://www.chickens.allotment-garden.org/keeping-chickens/keeping-chickens-allotment-poultry-plot/keeping-poultry-allotments-legal/