A real how long is a piece of string question.
It is perfectly possible to feed a family on £50 ish per week if you are prepared to shop around, cook from scratch, buy what is on offer/in season rather than sticking to favoured brands, eat less meat and fish, moderate alcohol and treats/ready meals, use up leftovers etc.
You could also eat absolute rubbish (farm foods value pizza and chips etc) for a similar amount.
Similarly there are people who will argue to the death that it is simply not possible to feed a family of 4 for less than £200/300 pw, but for that they will be shopping in Waitrose, lots of prime meat/fish, imported fresh berries and out of seasonal vegetables, naice ready meals and nibbly bits (olives, anti pasti etc), lots of branded cleaning products, more alcohol, etc etc.
Depends how much time you have, what sort of food you like, what priority you put on different types of meals, how much you waste, what shops you have access to, all sorts of things. But to answer your question, somewhere between £50 and £300+ pw is reasonable depending on your circumstances. At your income level, unless you have a huge mortgage and/or debts, I would imagine that you are at the level where you have some but not loads of disposable income and saving, say £50 pw on groceries could make the difference between being able to afford a holiday or other treats/luxuries - spend loads on food - little money available for other things or spend a bit less, but still enough on food, have money available for holidays, treats or luxuries.
If you were on a debt management plan, there are guidelines as to what is appropriate to provide an adequate, sustainable but not luxurious amount of groceries and I think this is about £120 pw for a family of 4.