I am not in UK so I cant comment on warmth, but hit some difficult times financially due to divorce, and this is what changes I have made:
Instead of buying prepacked mince (which has become a staple meat along with chicken) I go to the butchery section of the supermarket, where it is slightly cheaper per kg, and ask for the amount I need, ie 900g, but split into 3 x 300g bags and freeze these. I have found that using less meat and adding grated carrot, oats, and other veg, stretches it out to the same as 500g of meat.
I only use half the amount of washing powder than I used to, so about quarter of what they recommend, and still the washing comes out just as good. Same with dishwasher tablets, chop them in half and they work just as well.
I realized just how much fruit and veg was getting wasted as I bought too much at one time as was perhaps on special. It doesn't work out any cheaper as they go to waste. So now I just buy more frequently, but smaller amounts, the 'specials' are not always quite as special as the shop makes out. Although they are great if you have a group buying scheme so you can split them, but I don't. So things that could be used up although looking a bit rough (apples, go into apple sauce or pudding), veg, gets made into soup or if really bad boiled up and mixed with dog food for the dogs. And I only buy what is in season. I love avocados, but they are not in season now and I will not pay that overpriced amount for them, so no avo in salads for me right now.
We were wasting a lot of bread, as I don't eat it, just the dc. So bear in mind it is hot mid summer here now, so leaving a loaf out for a few days, goes moulding quick in the heat. So now I freeze the bread, and dc just take out the slices they need. So if they need sandwiches for school, either they have to remember to take out their bread the night before, or make a frozen sandwich. (bonus is, teaches them to be more responsible for their own lunch). Milk, I also freeze and take out only when last 2 litre is nearly finished, as goes off to fast in the heat. (although you don't have this problem right now, may help you in summer). I don't buy butter, only butter spread. We cant spread butter from the fridge, its too hard, and we cant leave it out as it melts and goes rancid. Since I changed, they haven't even noticed the difference.
Cheese, I buy in 1kg blocks and grate up into 250g bags and freeze. Just take out one bag at a time. This is as ds would just be cutting chunks of cheese off for a snack, and not sure about for you, but here, cheese is more expensive per kg than meat.
Take aways only once a month, and if I am feeling generous will get dc Burger King or something after school every now and then, not like we used to, which could be once a week at least.
So, although I have made a few changes (there are probably more than I cannot think of right now), we have not one day gone hungry, or have our clothes looked grotty after washing. I just have to be a little more organised and prepared, and I do seem to be in the shop a bit more, but I go alone as I know what I need to get, and I stick to the list. Taking dc with you is a recipe for disaster for getting distracted from the list.