The Money Saving Expert forums have a section called "Old Style Money Saving" which I suggest you look over. They have a grocery challenge which, even if you don't participate in, could give you ideas. There are areas of the site which can be a bit...fighty, but in general, it is a good place to get advice even if you don't slavishly follow what some of the people do there.
I use mysupermarket, but I generally get Ocado/Waitrose. If you're not careful, it can be more expensive, but it can also be cheaper for some things. For instance, we're ordering a big 5 l jug of Ecover from Ocado. It's an initial investment, but dirt cheap in the long run. I think Waitrose/Ocado are the only ones who offer it. We have used Sainsbury's delivery, but didn't really find it all that brilliant. The produce was a bit dodgey and they substituted things wrong. And the one time we shopped for groceries at Asda, we had milk bottles break, the pepper grinder we bought broke within a week, and my husband didn't like the quality of the meat. Sometimes things don't always work out to be cheaper in the long run, but it may be a YMMV thing with Asda.
We're trying to cut our grocery bill in about half without turning to stodge to fill up our plates, so I can understand how overwhelming it might feel.