I love Dominic's explanation!
Council has just been, and stated that we have to get rid of our chickens and downsize to 6
Your statement is contradictory. The council has either allowed you to keep hens, but a maximum of 6 - or to get rid of them. I assume it's the former?
If so, then they are not forbidding you to have hens, but restricting the number, presumably on the grounds of potential / actual nuisance.
Irrespective of what the neighbour may or may not have said in their complaint, the council has inspected you and made its independent decision. You need to move on from issues such as cockerels and ducks.
In my view, the council are wrong in their interpretation of the application of the Allotment Act.
The introduction to the Act states it is "An Act to amend the law relating to allotments and to abolish restrictions on the keeping of hens and rabbits". If the section on hens related only to allotments, it would be worded differently. The wording clearly indicates that the Act has two, unrelated purposes despite its general title.
Furthermore, sections 1 - 11 of the Act are headed "Allotments", whereas the s.12 heading expressly states "Abolition of contractual restrictions on keeping hens and rabbits". Again, if it was intended to apply only to allotments, it would a) have included it in the allotment section, and b) it would have used the phrase 'tenancy of an allotment garden' rather than 'any lease or tenancy or in any covenant, contract or undertaking relating to the use to be made of any land'.
However, as Hillfooter (I think it was) said, a court case over this will be unpredictable and costly.
By all means write to your MP but don't get involved in a court case unless you are prepared to spend money on it. It would be a case of principle because, as I say, they have not actually banned you from keeping hens.
Sorry for the long post but hope it helped.