I have a plot and am site rep on a council run site and we are not allowed chickens.  They are permitted on a couple of sites in the area, but you have to apply for permission.  This is their wording on the subject if it helps.

Chickens

Livestock may NOT be kept on allotments, EXCEPT xxxx and xxxx Allotments, where the keeping of chickens/ducks is permitted, with written consent of the Council and subject to the following special conditions, A- The numbers of chickens/ducks must be manageable; B-the livestock are well and humanely managed; and C- they do not cause any danger, nuisance, interference, disturbance or annoyance to Tenants or to anyone else including members of the public and the owners or occupiers of the neighbouring and adjoining property or plot holders. The Council may decide that keeping livestock on the site would be prejudicial to health or a nuisance and has discretion to suspend permission to keep chickens/ducks on site.

For what it is worth, my experience as site rep has mostly been positive, but I have had a couple of people of a similar mind set to your tenant.  Just telling people what the rules are is not heavy handed and if people are doing things without permission, you have every right to tell them there are consequences if they persist.  They are trying to ride rough shod over you and make their own rules and that is just not how it works - either for allotments or life in general.

I would say stick by your guns and tell them if they continue to do so, they risk eviction.  You don’t have to actually start any steps to do this.  That may be enough to stop them.  If not, I would say go ahead and start the process.  You are not evicting someone for being flaming difficult, they are doing that to themselves 

This is our situation:
Our allotment site is fully self managed and allows chickens as part of the Tenancy Agreement.  We ask only that members ask permission first ( as a courtesy and so the Committee knows what is going on) and the rules stipulate an immediate override of a our rules by any DEFRA rulings.  The Committee don't police defra rules they just advise that they must be followed.

here's my question:
As a self managed site are we subject to the Allotment Act 1950?  Can members just bring chickens to the plot anyway, as of right?  I can't find anything of substance online.  The answers are not on the NSALG site it's all  Allotment act 1950 with them and in an ideal world there would be no problems.

But we have this one member...
We have a member who is quite a determined individual.  They bring their chicks to the site everyday with out asking permission and they have list "informed" us that they will be a permanent fixture quite soon.  We are not a heavy handed Committee and we can't police the site daily nor would we want to.  We want this member to enjoy their plot and chickens and they keep a good plot.   (But this person would call the sea stupid and tell it to make it's mind up. In or out, not all this fussing about.)  I don't want this member getting the site into trouble especially with the new registing rules.  But they hate being told what to do. and I want to be able to have the treat of a chicken ban if they  muck us around but i don't want to use other rules which would mean eviction. We only chuck people out for doing nothing and being a problem to other members, not for being flaming difficult.

Every morning I need to remove a slug, maybe 1 - 2 cm long and about 3mm wide, from the house near the front or rear door. No doubt the extremely wet weather is to blame along with a slug's ability to shrink its width by about 80% to get under doors. Anyone else bothered by these slimey little things getting in the house and leaving glistening trails?

Rain overnight but a bright sunny start to the day, it didn't last long.  There was still a bitter wind and it's brought the clouds over so now it's grey, dark, cold and windy. Lovely  Just missing some rain to make it utterly miserable.

Like MOS, a bit dowly here and there maybe a little shower later on.