OP it's a lean holiday and I'm sure you can do it but for me I don't want to be scrimping on holiday . Let's hope it doesn't rain for the week or a week stuck in a caravan will be horrible .
Well good on the OP for giving her child a holiday on a tight budget, rather that than no holiday at all. The child will remember the time spent in a lovely place with their Mum, not that they didn't have access to bottomless ice cream.
If it rains then you just make the most of it. Maybe pack some board games, a pack of cards and a jigsaw OP. Plus wellies and waterproofs and embrace the showers.
We went to Cornwall as kids when we didn't have much money - I wasn't aware of that at the time, shows that my parents just didn't make a fuss about the lack of funds. One of my fondest holiday memories was eating a proper Cornish pasty fresh and still warm from the bakers. I expect they aren't cheap but they are filling and traditional.
I also wouldn't worry about being totally wholesome for a few days. In fact if there are things you don't normally allow, they can be allowed on holidays and can be seen as treats. Tinned hotdogs are one of my guilty pleasures even now! A bag of chips by the sea - don't need fish if the budget won't stretch. Greggs sausage rolls are another usually avoided food I indulge in when travelling. We weren't big fans of MacDonalds for the kids so on the rare occasion they had one they saw it as a big treat - even though for us it was one of the cheapest meals we had. They also took a cereal variety pack each as we never had sugary or chocolatey cereals in the house and they loved it.
Beans on toast is a totally acceptable lunch or light tea. Ditto things like 'big soup'
Pasta and a jar of sauce is a quick and easy meal.
Picnic lunches have their own appeal, even if it's not warm enough to sit outside and you end up eating it in the car. I had some large plastic plates I used to take on holiday for picnics - saved a bit of the mess in tbe car.
I'd front load the self catering /cheaper meals, save eating out for the end of your holiday. Partly because it's nice to end the time away with a treat but also if there are any unexpected expenses, you still have some budget left.
I would want that much per day for meals out and activities plus random spends for snacks, whatever the kids want.
That's ok if you have that kind of a budget. Not everyone does, hence this thread, so that is not a very helpful comment.
OP, given that your budget won't allow for 'whatever the kids want', maybe allocate your 7 year old £5 a day for treats eg ice cream/sweets/amusement arcade/comic . If they don't spend it all, it rolls over to the next day so they can have something a bit more expensive. That way they get a treat but don't expect whatever they want.
Have a fabulous time x