I just spotted a pot about this on Chris Slade's Bee Blog http://chrissladesbeeblog.wordpress.com/2011/01/13/bees-on-allotments/ .
I've had bees on my plot for ten years, mostly illegally. Originally, Birmingham allowed a couple of hives on a plot, but there was a row about someone keeping very bad-tempered bees on my site, and it caused such a ruckus they were banned. It was a long time ago now, and the rule was recently relaxed. You're still supposed to check with the Allotments Department.
My view is that it shouldn't be a problem, as long as common sense is applied. In any situation with close neighbours, temper should be a priority. Most sites are open, and people are likely to be working or passing within a few yards, in full view of the bees. I have hedges, which makes a lot of difference, but there's still no excuse for nasty bees. Low swarming should be a major consideration as well; swarms may do no harm, but they do frighten people. They make extra work for the beekeeper as well.
Then not too many hives should be kept. I can see a potential problem on some of the sites in London, where plots are about the size of a tablecloth, and in this case the answer might be to set aside a quiet corner of the site rather than having hives on individual plots. At the other end of the scale, my plot is very large, with six-foot hedges, and has more scope than most. A couple of hives on the average open plot is probably about right.
In ten years, I've only had objections to my hives once, and that was from someone who was openly trying to drive me off the site. I had a letter from the Allotments Department years ago, pointing out that bees weren't allowed, and asking me to remove them 'as soon as possible'. Somehow or other, it never became possible, and as the letter was never followed up, the bees were never removed. I had the impression at the time that they weren't very interested! Apart from that one incident, everyone has always been quite supportive.
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