I'm the other way around, I find cash doesn't get accounted for as easily, whereas plastic means I see the total each month and see what we spend more / less on.
Just be careful with Aldi and Lidl, as they can seem cheaper for example if you are someone who buys "a bag of apples" you may think you are paying less but when you look at the number of apples or size of them they are much more expensive than for example sainsburys basic range, and the apples aren't anything like as nice. I'm guessing that sainsburys use whatever apples they have in surplus for the basics range, as it changes through the year, but usually it's a really nice apple between a cox and braeburn taste.
Same for lots of the food, I use the price per kg option to compare loads of different fruit and veg, and Aldi and Lidl are occasionally nearly as cheap as Sainsburys basics, but usually more expensive, which works for a lot of the food we buy.
If you drink or are a brand name buyer then Aldi and Lidl probably are cheaper, but I've checked a lot of products price per kg or per item size quite a few times, and we'd pay a lot more in Aldi than Sainsburys, and can't walk there, so it's even more expensive in the long run. The way it works is you can feel like you are getting something cheaper as their sizes for things are often smaller. So "a pot" of cottage cheese is cheaper, but the pot is much smaller than the size we normally buy so it's only cheaper if we then eat less (unlikely
That could be an area / typical shopping list specific thing, as I know lots of people swear by Aldi etc, and we used to shop there all the time and find them loads better than the supermarkets when we lived in wales - but at that stage we were comparing with having bought brands rather than supermarket own brands. I'd love it if the adverts actually were true for me, as I'd like to spend less, but the local ones here are usually quite a lot more than sainsburys if you compare like with like for things like carrots, tomatoes, apples, sliced ham, cottage cheese etc. And sainsburys wins hands down on the quality.
Whether that works for the other supermarkets don't know but I know last time I checked Tescos middle range, which we find more equivalent to sainsburys basics, it was also usually same price or cheaper than Aldi for the things we buy.
I find best money saving in the supermarket is mainly ignoring the deal stickers, and working it out purely by price per kg, unless I actually WANT two or three of the buy one get one free / half price items. I've been sad enough to work it out quite a few times, and usually it's not actually very different in price, it just looks cheaper / better value. Especially as someone said earlier, with bigger boxes. It used to be that buying in bulk saved money, but I think they have clocked onto that now, and often it isn't such a bargain.
The cooking more from scratch and eating through the week bit makes a big difference as people have said.
The other thing for eating out is checking out the light bites or child portion type menus - quite often the serving size isn't actually much different, but the price can be, and it's a godsend when out with people who have a lot more money and choose somewhere relatively expensive as you can choose something reasonably sanely priced without it being too obvious. Being overweight I can use the excuse it's for weight control, though this rarely holds up as an excuse as I do often then have pudding...