I don't see how you can spend so little if you weren't being extremely careful and disciplined
If you eat very healthily then £60 a week for 4 is doable without being stingy IME.
Breakfast for us is cereal or porridge usually, with a piece of fruit - about £6 a week I reckon. Lunch is sarnies, salad, fruit and yoghurt, eggs or sardines, sometimes a tin of soup or beans for convenience - i'd estimate about £20-£25 a week. Salad and fruit is dirt cheap if you shop at Lidl or similar.
Dinner is where you can hoik the budget right up if you don't have time/fancy something 'nice'. Our staples are things like tuna pasta bake, spag bol, pork loin with noodles and veg, jackets with various fillings, sausage or chicken casserole with rice or spuds - all healthy and full of veg and can be made for £5 a meal or thereabouts. Something like a spag bol or chicken casserole is slightly more for decent mince or chicken breasts but will do us for two meals so evens out.
We probably have paella about once a week - and I buy Lidl frozen paella which is £2 a bag (and two bags does us 4) - I don't buy a lot of ready or convenience food and for those I do, i'm a serial ingredient checker and the paella Lidl does passes my ingredients test and is bloody lovely.
The times when we spend more is when we buy a lovely dessert on a Sunday, or get a big joint of beef (which we overindulge on), or buy ready made lasagne's or ready prepped veg. All of which are either convenience or just over-indulgence and not particularly great for you anyway.
If you're not prone to overindulging and you're not strapped for time or (in our case) not just occasionally lazy then it wouldn't be a struggle to keep to £60 a week without particularly trying.