Eat less meat. No need to go vegetarian unless you want to, but eg make a bolognaise with half as much mince and add more lentils and beans to pad it out a bit. I do this for health reasons but it's also a money saver.
I think meal planning and eating up leftovers is the best tip. Aim for zero food waste.
Things like rice and pasta are sometimes cheaper in huge bags, if you have storage space. Ditto sacks of potatoes from the farmer.
Eggs and porridge oats are cheap and nutritious. I make my own porridge and flapjack. I also make my own bread in a bread machine but I appreciate the initial outlay of £100-odd for a decent breadmaker might not be an option (Panasonic are the best by far and worth the extra IMO).
My local greengrocer is much cheaper than the supermarket, less convenient though. And I know not every town has one. I like to support the small family business too.
Buy fruit and veg that are in season. No need for it to be boring necessarily if you are imaginative with root veg. In summer you can buy the berries etc and freeze them (also pick blackberries) or make jam.
The food thing takes more time and planning but definitely there are savings to be made.
For short journeys if possible leave earlier and walk there instead. I appreciate this is not always an option - depends where you live. Every journey I walk I think I am saving on bus or petrol (also for me there are health reasons for adding more exercise, though I genuinely love walking too).
We use a basic spreadsheet to keep track of our budget, knowing your outgoings is very empowering.
Good luck