You don't need satellite in the UK, Freeview works in most places. If you want to be certain of getting a signal then consider Freesat. Freeview relay stations only give 14 stations where main stations get 80 odd. Freesat will get you the same as a main station. If you want to do it cheaply get a Sky+HD box (or better still the multi-room version which is smaller and lighter) and a Freesat-from-Sky viewing card - once off £25. Freeview comes in through your caravan TV aerial but you need a dish for satellite - see below.
If you go to Cash Converters you will pay less than £20 if not less than £10 to get a used Sky box with mains lead, remote, and a guarantee. If you are lucky it will still have a viewing card in it which will allow you to get almost everything you want of FTA (free-to-air) and FTV (free-to-view) channels (then you won't need the £25 card!)
You will have difficulty using the smart facilities of a TV as your chance of getting a fast enough broadband connection through the site wi-fi is next to zero. You can use a mobile wi-fi unit (a.k.a. a mi-fi) which will get you broadband through a cellular phone network but such data does not come cheap.
If you want a TV for the van and haven't bought one get then forget about smart. You can get a 32in (if you have the room) LG TV (which is actually smart) that has both Freeview and Freesat tuners built in for about £180 from Currys or Richer Sounds. Otherwise get a reasonably sized TV to suit your van layout - 24-28in for example - that has a HD tuner (Samsung and LG do both) and you are on your way.
If you decide to go down the Freesat route you will need a 'Sky' dish with a standard LNB* (the bit on the end of the arm) and a tripod of some kind. The dish does not need to be high up - so long as it has a clear view roughly SE it will work on the ground! You will also need some aerial cable (which you can also use with the pillar feed on sites that have such) and a bag of F-type plugs - Screwfix is your best bet, a bag of 10 plugs from there will cost you less than a pack of two from a DIY shed or a caravan shop.
*Make sure it is a standard LNB, not one for Sky-Q which will not work.
There is shed-loads of info on line on how to make up the cables and how to align your dish on site - an optical compass and a signal finder (a fiver or so at Aldi/Lidl when on offer), and some pegs to make sure you tripod doesn't fall over will help enormously.