Ooh I'm jealous, I love the Explorers' hotel - we've only stayed there for one night but loved it and will be going back

I agree that you can defintiely take food with you in your suitcase/hand luggae (though check for any specific restrictions) - the first time we ever went we were pretty skint and nearly bankrupted ourselves to go, so had little to no spending money whilst there - we took nearly an entire suitcase full of snacks like instant noodles etc to make with the kettle in our room

the kids didn't mind, it was all part of the fun!

However, you also asked if there is a supermarket nearby - yes, there is the Auchan supermarket in Val D-Europe, which is about a 20 minute walk or five minute bus ride from Disney Village - its very affordable and has a large range of "own brand" stuff - its not premium Disney prices at all.
I don't think you mentioned how many children you have but £1200 should be more than enough for food, snacks, photopasses and spending money!

Of course the restaurants vary in price but we found it easy to get a decent meal for 4 for around 100 euros. The Explorer's hotel has a really nice "all you can eat" breakfast, so I'd advise that you stuff yourselves full, stick to only snacks during the day (which if you want to save money, you can bring with you, or get from the Auchan, the garage bythe Santa Fe, or the railway shop) and then have a large evening meal in a restaurant.
We usually get an evening meal after the parks close, there are plenty of great places in Disney Village, and that way we don't lose time in the parks. However, if your kids are younger, this may not be an option. Also in the Village there are places for a cheaper snack or smaller meal - Earl of Sandwich does a really good set price meal, and of course there are places like McDonalds and StarBucks which are pretty much the same prices as here. You mentioned that you like Burgers and chips - I'd highly recomend Annettes for those, and it is very affordable - around 21 euros each for a main, desert and drink. Billy Bob's is even cheaper, around 13 euros for a main, desert and drink, and it often has free entertainment - live bands etc.
Also worth mentioning that there are 3 really good and affordable restaurants in the Explorer's hotel itself - cheaper than most places in the parks and village, good quality, and of course less busy and less queues. The pool complex there is excellent and the restaurants are all around that area. I know that the next time we stay in the Explorer's hotel we'll definitely be taking advantage of the pool and the Pizza place right next to it

For character dining, its slightly more expensive, but Cafe Mickey in the Village is affordable and has plenty of characters. If your kids like Princeses, I'd highly recomend Auberge de Cendrillion character dining in the Disneyland Park, though its quite pricey - around 160 euros for 4 from what I remember.
To give you an idea on spending money for kids, the first time we went we gave our kids 20 euros spending money each and advised them to think carefully about what the wanted to spend it on - remembering things they liked the look of each day, then making their decision on the last day. They got a nice souvenier plus some small things like pens, magnets, sweets etc with the change. In later trips where we have been more affluent we give them around 100 Euros each with similar advice - they can get plenty of cool stuff for that - for example last trip my son got a large star wars toy (vehicle), a tshirt, a light sabre and lots of small things like pens, keyrings, sweets etc. My daughter got a hat, t-shirt, snow globe figurine, bag and some cheaper stuff again - they certainly didn't feel hard done by. Even considering other stuff they also had their eye on, it would have been hard for them to spend 200 plus without feeling over extravegant...
Remember also that if there is any "big" thing that they really want and you can't afford, you can often pick it up on ebay, from Disney Store, or even through mail order directly from Disneyland Paris once you get home! We have found it useful in the past to take photos of items and then their price tags with our phones so that we can remember to get them later if we still want them
