We do a big shop every 4 to 6 weeks and then just shop for fruit and veg as we need to (usually at local market). We both dislike food shopping so suits us plus if we go to a supermarket more often we just buy more items!
We finding buying in bulk works out cheaper but, of course, you have to have space to store it all.
Both me and DH are vegetarian so that makes our food bill much cheaper anyway. We buy big packs of lentils, chickpeas, different types of beans, rice etc from an indian supermarket because they are so much cheaper. We also buy our spices and things like coconut milk from them.
I have a rough meal plan for a month and make sure I have or buy the ingredients I need. I often make double of things like lentil bolognaise, bean chilli, curries, shepherds pie etc and freeze one lot.
We cook almost everything from scratch which works out cheaper and we waste just about nothing. Veg past it's best can be made into soup or a veg stew or a veg chilli. I even use cauliflower leaves and stalks in soups or stir fries.
Bread past it's best can be made into bread pudding or bread and butter pudding or just made into breadcrumbs.
We buy any yellow stickered items we know we will use. Bread in particular is often reduced by a large amount. We split it into freezer bags and freeze, just take out what you need. We do the same with milk.
Freezer bags can be washed out and reused time and time again.
I buy the cheapest bath wash I can find (usually in Wilkinson) and fill up handwash bottles.
If you have a local market and can get there buy your fruit and veg there. If you can get there just before they pack up they almost all sell off produce very cheaply