Do you mean just to shop ?
If so......then as long as you dont obstruct anyone else then of course you can park there.
I certainly don't think you would have to ask permission to park your van if you were SHOPPING there !
I usually go to the far end of any supermarket carpark at a hopefully quieter time and try to make sure I can get out when I return......some people just do not think and very often park right up against you when there is loads of space elsewhere :roll:
My local tesco has a 3 hour limit but I have actually overnighted on other ones that hadn't restrictions.......when visiting friends etc......I have asked permission before but I know it depends on the parking restrictions of the various different stores as to whether they allow it........
My daughter is a mobile dog groomer and her van is bigger than yours and she has no problem parking regularly to shop in the Axminster/Honiton/exeter areas.......so please don't worry about it I am sure you will be fine
Lynda