We have an allotment and it’s fairly relaxed as far as rules are concerned. We can even keep chickens and goats if want. Allotments have differing rules and charges depending if they are National Allotment Society, Council Owned or Private Landowner. Some allow livestock, some let you burn sticks and dried cuttings etc. Our last allotment didn’t allow greenhouses because of the glass risk.
As far as taking your piggies and putting them in a secure run while you work is fine, but do consider if the previous owner has used weed killers and pesticides? Also other animals such as dogs may well be there with there green fingered owners too.
The best thing to do is grass seed an area of grass, let it mature and place your run on it, then you know that the grass is fine to eat. Allotments are a long term plan. But you can start preparing for next year and do most of the groundwork in the autumn when it’s a bit cooler, unless you have been lucky enough to take over a well managed plot