I don't know about the UK, but the basic principles are always about planning an appropriate menu to re-use everything, cooking from scratch and avoiding most boxes/partially-made stuff, planning the menu around what is cheapest (which is usually what is in season), and making expensive ingredients the "treat"/accent vs. the core of the meal.
I am also working at getting grocery spend back under control, and it's not hard, it just takes discipline. Every Sunday, I have to plan out all of the meals based on what is cheap, thinking through how I can re-use the same basic ingredients in different ways (my DH detests leftovers, so I have to make it look like something different most of the time). Then I have to cook or partially cook much of what I buy so we are set up for the week. So e.g., I grill up a mess of chicken, peppers, and onions on Sunday for fajitas; then I eat the leftovers every morning in omelets, and I have at least one other family meal of quesadillas from that as well. Last week it was chili, which served twice by itself, twice as a hot dog topper when we needed a quick dinner, and made a lovely base for some eggs this morning to boot (and we still have several meals' worth left, which we will actually eat because DH is out of town). All from about $8 worth of meat, $1 can of tomatoes, $1 beans, and maybe another $1 in onions and other veg -- oh, and a beer. So under $15 easily. But it does take time, and thought, and avoiding the temptation of that super "thing" that looks tempting in the store but isn't on the list.
The hardest part has honestly been being realistic about what we will eat and avoiding waste. I am notorious for buying lots of greens and planning healthy salads. But the problem is I don't actually like salad very much, so they sit in the fridge until they rot. Or sometimes I plan to cook four nights, but then we have so much left that I never cook one of the meals and it hangs over until the next week, when the produce is starting to look dodgy. So I am re-training myself to buy less up front and focus on using it all up, supplementing from the freezer/pantry if I run short.