Yes, Julian! That's the problem!
Turn up with any sort of trailer and some sites will charge caravan rates - AND extra for the tiny backpacking tent you are actually sleeping in. These are usually the sites that charge per plot - one for the "caravan" and another plot for the tent,how ever small. One site tried to charge me a flat rate for an electrical hook-up even though I had nothing to plug in!
This is why I suggest you ring the site in person before committing yourself.
Having said all that I've only had problems with the larger sites run by staff taken on for the summer. They tend to follow the rules laid down by the Management to the letter. Most places, wishing for repeat custom, tend to be more flexible.
Grumpy Old Man comment!
Stick to touring sites.
In high summer I agree with Sartre: "Hell is other people!"
I avoid large, permanent sites like the plague, especially those advertising "a range of activities for children". They can include lethal "playgrounds", ill-maintained and unsupervised, where your children will be ridiculed for talking "funny" (mind you, that happened to MY kids in Cornwall. Their Northern accents being remarked upon disparagingly by a gang of little twerps from the home counties). Urine and slime-filled swimming pools are not unknown - just try keeping your kids out of one on a hot day - and you might well be bothered at any time, day or night, by enthusiastic young people in clown make-up trying to sell you tickets for a barbecue scheduled for the day after you leave. (Bear in mind that a student in charge of a barbecue in France ,Italy, or the UK, is hardly likely to have read any of Elizabeth David's books, so adjust your expectations accordingly! )
Hope all that doesn't put you off! Ha, Ha !
Whingeing apart, I've camped since a teenager (mostly backpacking or cycle camping) and towed my Swallow Boats Cardigan Bay Lugger for thousands of miles in the UK, France and Italy and rarely met with any unpleasantness at all.... but don't get me started on airports!