If it is an actual firepit, yes it would work for a dutch oven. That is if it is the kind you put logs in.There are quite a few campsites that allow fires, though most of them they have to be in a firepit off the ground (so probably still not suitable for a dutch oven) This site is one of the best for UK campsites and allows you to filter on all sorts of parameters, I use it a lot.
I think what I love most about camping is that there's no right or wrong way so it can be whatever you make of it Now we have the motorhome we do have a TV - its nice to be able to watch a film in an evening when its mid-December and its cold and pouring it down out there and the pub is too far away to walk to.
Here in Texas, most state park campsites have both grills (you would call it a griddle) and firepits. Now whether you can use them depends on the county and what the weather has been doing.
Grill here fire below, food on top.