Runner beans plants decimated up to 4 feet

We have a problem on our 48 allotments.  

Everyone's runner beans, peas, beetroot leaves and sweetcorn are being eaten.  The beans are totally decimated up to 4 feet and the tops left intact.  The leaves and beans are all eaten but the main stalk and the leaf stalks are left.

Deer come onto the site (in Bath, Somerset) but they would not stop eating at 4 feet, though I suspect them for eating the beetroot leaves and sweet corn.  There are no hoof prints and no droppings evident either.  The tops of the runner beans continue to grow and are left untouched.

Some people have reported seeing a badger on site but that is a heavy creature that would push over the canes, and there is no damage to the canes.

Magpies land on the beans but are only likely to pick off a few flowers at the top.

It cannot be slugs or snails as everything has been eaten, and across all allotments.

I have asked the council to install a high fence to keep the deer out, but I don't believe they are the problem.  What is causing this damage?

Vernon Herridge wrote (see)

...Deer would not stop eating at 4 feet...

Deer come into my garden and they do stop eating at a very precise height.

I have some ivy covering a wall. The ivy is striped upto a particular height, and untouched above that height. It's very characteristic of deer damage. Though the 'deer line' is more like 3 feet. And, as you say, there would be tiny hoof prints (they are very small).

This sounds exactly the problem I had last year and it was deer because we saw them early in the morning. They ate all the spinach too. We have small roe deer who roam in twos and threes. We put up a high wire netting fence and bingo! no more damage. This year we've had the best runner bean crop ever.