A few ideas.
Do you have a freezer, or can you get one in the meantime (somewhere like Gumtree or Freecycle might be an option)?
If that's possible, start keeping an eye out for short dated meat, in particular, and veggies too and freezing them. Also bulk deals on meat - some butchers do a "1 week pack" of say a bag of mince, 5 chicken breasts, 4 pork chops and some stewing lamb for €20. I wouldn't use all those in 1 week, but it could be worth buying the bulk pack and freezing lots for use later in the week or other weeks. Or take advantage of good offers on foods you use anyway - so BOGOFs etc - freezing or otherwise saving the additional.
Use bits of veggies to make a stir fry - so the last rubbishy carrot, a withered pepper, a couple of florets of cauliflower and an onion can make a decent either side dish of veg or the basis of a dinner with a Chinese or curry sauce.
I often do a side of roasted veggies if I have anything cooking in the oven - dice up onion, garlic, pepper, mushrooms, courgette (aubergine if I will get away with it), tomatoes. Season well, including a good glug of olive oil (doesn't have to be extra virgin) and roast for maybe 25 mins. Leftovers are great frozen to use as a side reheated, use in tomato sauce with pasta, put into a quiche, in a frittata, all sorts of uses. And while I tend to do it frequently enough as a planned side to roast chicken, I will throw together a small batch when I have a few withered bits needing using up or see a glut of suitable veggies going cheap in greengrocers/SM.
And learn to make bulk batches of dinners that can be frozen. So make a spag bol with a few extra carrots blitzed into it, or even a mix of veggies (courgette, mushrooms, peppers are nice for Italian, but also butternut squash and lentils work well for bulking up), and doing it from an onion, garlic and tin of tomatoes rather than a jar of sauce. 1lb of mince beef can make dinner for 6 instead of 2-3 that way. Eat that night's dinner, but portion out the 2nd night's dinner into freezer container before plating up to reduce "oh I'll just have seconds as there's loads there" type eating.
Frozen veg are also quite often quite cheap and are generally as good, sometimes better, than fresh. So having a freezer means you can have a few bags of frozen veg on hand always, less waste than preparing veggies, and you only need to take out exactly what you need for each meal.
Now is the start of the growing season too. So try to get a few seeds into whatever ground you might have, or even a plant or 2 from garden centre - to either cut costs over the summer and add to savings, or to freeze the produce and use that when the money slows down. Things that are good would be courgettes (get loads from 1 plant), broad beans (freeze well) and French or runner beans (also freeze well), peas (grow along a fence and you can get a lot), Brussels sprouts (long season but ready in late autumn/winter), broccoli (lots off a single plant as there are lots of side shoots), spinach or other salad leaves to eat as baby leaves (pick and eat all summer), and tomatoes (cherry tomatoes are best I think, and bush type plants grow well in hanging baskets, cordon plants grow tall - garden centre will help identify which).
Do you have a local butcher? Learn which cuts of meat are cheaper, like things that need long slow cooking etc. Things like liver and kidneys are also good once you know how to cook them well rather than just make them taste like cardboard. (You may also get bones for making stock - so a handful of mushrooms and a cup of rice with a decent chicken stock can become dinner, or lamb stock to make a really nice lamb curry etc).
Look out for an Asian supermarket too. They will have lots of seasonings like dried herbs and spices much cheaper than regular SMs, often do cheap veggies and fish, have large bags of rice and noodles which are much cheaper than SM too, and things like pastes and marinades and tinned ingredients (coconut milk, chickpeas, bamboo shoots, beansprouts etc) that you may not get or only in the expensive ethnic foods aisles of SM. I save a lot of money this way.
Learn to make things from scratch. So Chinese may actually be very cheap when you make the sauce using cornflour, water and the proper spices rather than a jar of chop suey sauce. Or Italian tomato sauce. Or Mexican chilli con carne (or even vegetarian chilli).
One thing I spend a little more on is getting fully mature or vintage cheese - because the flavor goes a heck of a long way further than mild cheese. So a small handful in a large pot of white sauce is enough, rather than half a block or more of milder versions. It does work out cheaper in the long run. And I grate it for use in sandwiches or over melts rather than slicing, as that also makes it go further.