I buy some Tesco organic stuff and still manage a week's shopping for two (hungry) children and me for around £80-90 per week. This is includes lunches/packed lunches and also household supplies like cleaning materials, soap powder etc, a lot of which are higher-cost makes which I buy for ethical reasons, and pull-ups for my DS at night-time. It also includes some gluten free things (pasta and flour) as I am gluten-intolerant. if I didn't have to buy these, my shopping bill would definitely be less.
We are vegetarian which does bring the cost down compared with meat eaters a bit but I think we eat well and I don't skimp in terms of quality.
I am very focused on the organic stuff I buy - eg milk, cheese, yoghurt and eggs for animal welfare and health reasons; the vegetables and fruit, which are most susceptible to pesticide residues (eg leaf vegetables, grains, pasta, lentils and flour etc). I always buy organic tinned tomatoes and organic beans. For other things, I will buy the organic variety if there is not a lot of difference in price but will buy the conventional one if there is a big difference.
I no longer buy everything at Tesco - eg organic free range eggs are much, much cheaper at Lidl as are fruit juice (not organic), pull-ups, nice-quality toilet roll etc, so I tend to go there once a month or so and stock up on the things there which are cheaper.
I also buy some organic stuff from our local health food shop if it is cheaper - again,I go there once a month on average and stock up on specific things. I buy some things from M&S too - they often have good quality cheese on special offer, for example.
I have definitely been able to to cut my food bill a lot while still buying good quality stuff, including a fair bit of organic food - it just takes a bit of shopping around and planning. I also buy very few ready meals and cook most things from scratch apart from the occasional ready-made stir-fry sauce or curry sauce (but using easy, quick recipes as I don't have that much time for cooking).
Also, the freezer is my friend. I try to make double quantities of anything I am cooking and freeze one batch, which saves time and money (and makes you less likely to buy a ready meal).
Keeping an eye out for stuff which has been marked down as it is near its sell-by date also saves me a lot of money - it either goes straight in the freezer or I use it to cook a meal/meals which I then freeze.
Hope some of this gives you ideas!