I have delivery savers for Tesco, Morrisons and Asda. I don't like the Sainsbos here because there is a higher than average chance of a creepy guy.
In my experience, a lot depends on the local depot. I found massive differences when placing orders for family members in other parts of the country and when on self catering holiday. It's worth trying them all out.
It also depends on your shopping habits. Tesco have a wonderful search function which means you can search for stuff that is gluten free, dairy free, halal, vegetarian etc which is great if you want to browse. It's not perfect but a help. From what I can tell, they are currently rebranding a lot of stuff and reducing the number of lines they carry so they may not have everything you want. On the plus side I think their customer service is completely the best.
If you always buy the same things then Asda have some great prices but it's fiddly to browse if you are not sure what you want but want inspiration. They also have the cheaper slots, if you use flexi slots if you are going to be in all day. They can be really weird about payment, though, and there's usually a few threads every Christmas where Asda have taken a ghost payment, which means that there isn't enough left for the actual payment to go through so the delivery is cancelled and the money is unavailable. I'm not sure if that is still an issue.
Morrisons are great for fruit and veg, but I've found their meat is often 'off' when I get it, though that may depend on the local depot. I have to go gluten free and they have a lot more choice. They also have a lot of local stuff.
Sainsburys have a lot more 'naice' choice, and if you get decent drivers then they are great. You can try dropping down a brand or changing around some of the cooking habits to cut costs.
It may be worth checking out Iceland as they do a lot of fresh food and household stuff, but they don't have a huge range.
I need to get a hobby, don't I.