Permission to keep chickens

Is this a council site?  If so then your tenancy agreement will state how many chicken you can keep, if the council want to change the rules then they must give you notice of this.

What do you mean about them joining the allotment association? If you have a committee who looks after the site then no one can join unless they are co-opted on by the existing committee or they are voted on at your AGM, have a word with your chairman or secretary to ask if they have been approached.

The Allotments Act 1950, s.12, gives you the right to keep chickens but this is limited by the duty not to create a statutory nuisance, which I suppose would extend to not keeping chickens in such a "place or in such a manner as to be prejudicial to health or a nuisance or affect the operation of any enactment" - e.g. a health hazard such as rats.

Are you sure that all tenants with chickens are keeping them in such a way as to prevent vermin being attracted?  e.g. metal feed boxes, removing feed overnight (or whatever else those who know about chicken keeping would advise)?

I am purely speculating now, but why would keeping the levels of chickens to 3 reduce the risk of vermin being attracted?  There's either foodstuffs or there isn't.

That being said, there has been an explosion of rats on our site this spring - and we have no chickens.  Therefore there must be additional factors going on, such as a mild winter and spring.  The council would have to prove a causal link between the chickens and the rats, rather than just rats appearing anyway.

On your particular question about joining the association, I don't see the connection.  The plots are rented from the council and not the association.  Therefore, by extension, the association does not have a role in setting the tenancy conditions and joining the association could have no impact on changing to a 3 chicken rule.  The council could change the rules without joining the association. 

There could well be a completely different reason for the council wanting to establish links with the association - a positive reason.  But don't let that get in the way of any conspiracy theorists!

Even if there were proposals to change the tenancy conditions, you'd want to see the evidence justifying the restriction on a right set out in statute.  The council can't just over-ride statute unless it can demonstrate that there was a statutory nuisance and that making the specific change will alleviate that nuisance. 

If the chickens have been present for years, kept in the same way without changes (e.g. to feed availability / storage), and there have been no rats in previous years, then evidence would suggest that it is something other than the chickens which have caused the rats this year ... like the spring weather.

invest in treadle feeders for your allotment chickens and train them to use them (simply pop a weight on the treadle for a few days. These work by a chicken stepping on the treadle and that allows some food to be dispensed. Rats generally aren't heavy enough to trigger the operation.
All my poultry food is kept in old metal dustbins (rats chewed through my plastic bins), and if you throw down mixed corn for them to scratch around after only throw a small amount that they will eat up straight away.