By "duration", do you mean like all 5 days of the caravan & motorhome show at NEC ? There was parking for MHs & caravans there this year, you had to pay for it (I think), no EHUs or other facilities so you need to be completely self contained. Judging by the number of hi-viz jackets, I think sneaking in (I guess that's the "illegally" you suggest) may not be an option.... With current perceived security threats, I'd guess an apparently abandoned vehicle might be viewed with some suspicion.
I don't have a problem with paying and I can be self-contained. The show is the London Boat Show which lasts for 10 days and our Trannie attracts a daily emission fee. We have looked in vain for a site within commuting distance which would be better if only because of the EHU. We are exhibitors and the accommodation and travelling cost are killers.
I've just asked the Excel Traffic Department and they tell me that camper vans are permitted - £20 per day - 24 hours. As it costs us £15 per day for car parking, that's a good deal.
Amazing family weekend with old steam engines, classic car displays, market stalls, and full catering and bar. And camping on site - Save £25 by booking in advance.