One of the lads I taught (many years ago) runs his own business recovering huge agricultural and business polytunnels all over the country.
I will ask him and see if he has any ideas about planning permission for the large structures - I guess once permission is granted it is unlikely to be revoked.
My allotment site (a privately owned and operated one) had no restrictions on greenhouses - sheds could be no more than 8'x10'. Polytunnels became increasingly popular and some covered a good 40% of one or two plots. (mostly people had greenhouses).
Contacting the land owner (the council in your allotment site's case) is a good move especially before making an outlay and doing the work. Hope it goes well for you.