When I had allotments down south, I also used to have an occasional bonfire of the masses of brambles that were there. They don't rot down and they take up too much space and just piles up.
I used to get miffed with some of the local residents who move so close to an allotment site that has been there for decades. They like the idea of looking out of their windows to look at their allotments but don't like some of the things going on there such as an occasional bonfire.
I can recall an allotment site, where I previously had a plot, being at the end of a residential cul-de-sac. Some of us allotmenteers (is that the word?) used to like coming along early on a Sunday morning to work on our plots before going off and doing other things. There was a padlock and chain on the gate which you couldn't help making a "clangy" noise when you unlocked it and went in. Several of the nearby residents often complained about it and we were warned about it and told that we might be banned from going to the allotments before 9-00am on Sundays. Several of the more timid allotmenteers complied but others of us didn't and nothing was done about it. That allotment site had been there for a good 50 years so why move right next to it then complain? It is like buying a house under a Heathrow flight path then complaining about the noise. Ridiculous.
However (back to bonfires), at this time of the year when we are approaching November 5th, everyone here seems to be missing the ideal opportunity. In At Albans, we used to have an big annual bonfire on a derelict allotment on the allotment site on bonfire night each year. For several weeks beforehand, the allotment-holders brought all their stuff to be burnt to the big pile that was gradually building up. The bonfire was lit early-ish to enable folks to get to the big organised display in the local park if they wished to go. The allotment bonfire was a sociable event and no nearby residents would dare to make a complaint about bonfires on that date.
Why not arrange such a bonfire for Nov 5th on your allotment sites?