The density of the units allowed on the site should have been determined at the planning stage. I don't think there is any law about distance between units; we all refer to the "20 foot rule" but the clubs obviously make their own rules.
A lot depends on whether or not you are allowed to keep your car next to your caravan. If not, then the caravans can be much closer together. This happens on some sites in Holland and Spain.
I have seen commercial sites so full of tents that the guy ropes were crossed. And tents obviously burn much more easily than caravans. You will probably find that (as is the case so often in life) you get what you pay for. If your seasonal pitch was relatively cheap, then you might pay for it by being closer to your neighbours.