Something that I have been wondering about, is that all of the photos of the circles that I have paid attention to, have lines across the entire fields, outside of the primary patterns themselves, which don't appear to have anything to do with the designs, except possible being used as grid lines, like graph paper, for whoever made them. I'm not a farmer, but I've flown over a lot of fields, and have never seen anything like that in so regular of a pattern. I also noticed that the largest of the design elements appear to center very close to a particular set of lines, and the rest have a lesser but related location.
I also noted that in a Wikipedia article, that it said that 90% of all of the circles have been in in Southern England, and half of those are within 9.3 miles of Avebury, a Stonehenge like ruin, which is still used for both a tourist attraction and as a site for pagan worship. To me, that tends to point toward those pagans as being the designers. Even in other locations, I would imagine that there are similar pagans around.