How large is large in terms of family? I wouldn't expect stewing steak to cost that much unless you're feeding 10 people? so perhaps you also need to think about what you're buying?
Eg lamb shoulder makes a great stew. Waitrose has whole lamb shoulder on at £9/kg. to feed a family of 6, assuming the bone is in, I'd think that £1.2kg would still be more than enough. Similarly, Oxtail, when you can get it, is about £7/kg so even buying a generous portion will be relatively inexpensive.
Must it be red meat? Chicken thighs and drumsticks are a lot cheaper. They can be cooked whole or go a long way if used as a casserole/stew and removed from the bone once cooked.
Obviously, any stew goes further if made with rice and potatoes, other root vegetables and beans/lentils to pad it out.
Will they eat pasta with meat that isn't the main thing? eg, a packet of bacon chopped relatively small and turned into a good tomato or cheese/creeam based sauce would go quite far. we use smoked chorizo rings as well - half a ring chopped and added to a pasta sauce with tomatoes and aubergines feeds 3 of us - with DH and DS eating ridiculous portions because they both do about a million hours of exercise a week.
Steak goes a lot further if used to make wraps/pittas etc. Caramelised onion, steak (in slices), topped with cheese on a toasted panini with some mustard and mayo for a sort of Philadelphia cheese sandwich, or we do chargrilled greens (broccoli, leeks, spring onions) with a bit of a "sauce" made from lemon, honey, garlic and chilli and then steak slices all in a pitta bread. I can feed 4 of us that with 300g of steak. Or, of course, fajitas with lots of peppers/onion/tomato and thin steak slices.
Do you eat fish? Frozen fish fillets work out well and can be used to make fish pie/fish cakes.