Depending on how many nights you want, I have a feeling you might struggle to find something all inclusive within your budget during school holidays. We looked into booking Lanzarote for July/August 2015 for 14 nights, 2 adults and a 13 year old and the majority were around the £3k mark. Then our 21 year old decided she wanted to tag along too, cos none of her mates could afford to go away with her, almost doubling the price.
The price mark up during the school holidays is ridiculous, plus I begrudge paying adult price for all inclusive once your child is older than 12, especially when theres an age restriction on certain activities.
Hopefully you'll prove me wrong, but good luck with your search

Thank you, i'm not too bothered by AI but my partner seems to think it would be a better option. I might rethink, of ask her to....

Balkan Holidays are showing some half dozen options for Bulgaria for this August (too early for next year), with 2 rooms AI; I entered "Any London" as the airport as you didn't give a preference. Visit their website & have a look at what's on offer, then go back around September, when the new summer season should be on sale...