The only place you really have flex is in the food budget, but I do understand how difficult it is to keep this down when you include things like wash liquid, shampoo etc.
We have been living off around this much for last 18mths and our costs are higher - but then I have been ebaying/carbooting and so on like a fiend to make up to 500 a month. Its cleared alot from the house but there is still more but its getting harder to make that much now.
My advice would be carefully plan the food, shop cheap - aldi and lidl are great. Learn when they reduce and try and shop around then. Eat veggie at least once a week more if you can. I have a veggie curry I do which satisfies everyone and also baked potatoes beans and cheese is another good one.
I also try and find free food - so at the moment we are just coming to end of the apples lots of people have in gardens. So a couple of crumbles and custard will fill everyone and less needed for the mains and snacks in the evening.
The expensive foods are snacks - crisps, biscuits, chocolates etc I have cut right back on these we have one six bag crisps, one pack of biscuits and one lot of choc for the week - we occasionally buy more but not often now. I always vary what I buy by offers if I can - e,g, sains six bag crisps 85p, if you are having a cheap week buy sains choc at 50p a bar and make rice crispie cakes with the kids using cheap krispies though. Make stew - not rich beef or anything but use left overs for a scouse type thing - onion, cook off, add stock cube with water, chopped carrot, potatoes (if you can mix starchy and new that is good as naturally thickens soup/stew) and then add a meat - can be roast beef or Lamb (although I appreciate v expensive) but also chicken or gammon from a joint which is really cheap . You can throw peas in at the end and its lovely on a cold day and as the meat is cooked is ready to eat when the potatoes are and its all in one pot.
I think you are right to use the envelopes for saving but do keep them safe and where no one can pilfer from them.
Don't be afraid to ask friends and rellies if they have slightly older kids if they have any clothes or toys they are looking to get rid of as this can help enormously, even if you give them a bit of cash for them its no where near the cost of new etc.
Also if you have a clear down of toys etc before christmas its a good time to sell of excess toys as people are looking for things around now for Christmas - I just sold an outgrown bike that was in reasonable condition.