The last time I towed a caravan was sometime ago with a Vauxhall Vectra v6 .
However I see you are looking at the Hyundai Tuscon which will tow your caravan no problem, but the fuel economy won’t be great. I have had the Tuscon Ultimate 1.6 TGDI since March and only get between 28mpg and 31mpg on a mixture of local A,B and motorway roads and 38mpg to 42mpg on a run. So I would expect you would get considerably less than these figures when towing.
I’m not sure what diesels are on the scheme But rather than thinking you can only afford x amount of advanced payment, It maybe worth factoring in how much fuel will cost and offsetting it agains’t a diesel.