It sounds like you're having a really tough time.
How good are you at meal planning and cooking? If you are reasonably competent, then I have two resources that I would recommend.
On Facebook, or she also has a book, there is "Feed your family for £20 a week". This has an 8 week meal plan, with shopping lists. There is plenty of variety.
At even more of a pinch, but needing a bit more organisation, there is Thrifty Lesley (just search for her website and meal plans). She has about 12 weeks of meal plans, for about £10 for a family of 2 per week. It's pretty easy to alter, to include children. Even if you did this for two weeks a month, you could save a lot on you food bills.
Even if you used these as a basis, and topped up with some extras from Aldi/Lidl, you could be able to save a chunk on your food shopping.
I'd also recommend the free app Olio, which allows people to share food and things for free. Often, it is things that Tesco would throw away at the end of the day, which can safely be frozen. I've got school shoes, a bag of clothes and toys from it, as well as food. It shows these by how close they are to you. I've only got the free version, which works very well. There are often toys on it, in my area too.
In terms of Christmas presents, I'd also recommend the Christmas bargains threads here. Often, there are excellent, time limited deals on toys posted there. I think we're on the "Cinnamon Bumss" thread currently.
Also, do you use a cashback website, like Topcashback or Quidco? If you are buying anything online, you can probably get some money back, which can be taken out as supermarket vouchers, or actual cash.
Best of luck!