Some things that I have found useful:
Assess your food waste levels, and meal plan based on what you have in the fridge that needs eating to eliminate any unnecessary waste of food you are already buying.
Freeze things! Buy bigger packs and freeze in portion sizes. Chop up and freeze any veg instead of wasting it if you have too much.
Be more mindful of cost per portion comparisons e.g. Go for bananas as fruit of choice more often! Rice over potatoes/pasta (when cooking the rice from a big bag of grains). If you can afford to invest in a rice cooker this can make a big difference.
Meat goes further without feeling like you are scrimping if you cut or bash it when cooking. Small strips/pieces in stir fries, risottos, soups, paellas go further than chops/steaks. Pork and chicken go a long way if bashed and breadcrumbed - you can make a lot of your own breadcrumbs out of bread ends. Sausages in chunks in a ragu for pasta goes further than when whole as sausages and mash.
Download and check out Olio, bearing in mind most food gets listed in the evenings. Variable depending on area and day, but can usually help reduce your bread based costs if nothing else.
Prepare and bring food with you wherever possible when leaving the house to avoid on the go purchases. Work lunches, snacks and drinks for outings, picnics/sandwiches for days out.
Check your fridge and freezer temperatures, as food can last longer than you think if they are set to the right temperatures.
Use basic sense checks on food rather than relying on printed dates on them.