I use Tesco, started when I couldn't drive (thanks DVLA) as it saved my DD having to come & take me shopping. Useful for a monthly shop of heavy items, I still use it now although I can use my car again. Great for heavy & bulky items like cat litter, cat food, tins, fruit juices etc. I only buy packs of fresh chicken breasts & never fruit & veg. I am lucky that I have a good local shop & he delivers free, their fruit & veg is locally grown & good quality, I can also order meat there. I am lucky that we have butchers & greengrocers who sell locally produced where possible.
I select the cheapest delivery slots, no bags, I have a small kitchen so I meet the driver at the door as I have plenty of hessian bags, it is only a short walk into my kitchen & I can unpack at leisure. I also refuse substitutes, I'd rather be without than get something unsuitable. I find it great as you can keep a track of your spending as you order making it easier to stick to your budget.
Not sure which other supermarkets deliver as I live in a rural area, haven't used Iceland as shop is difficult to get to in my nearest Town, why can't they do on-line where I live? My advice, give it a try, try as many as you can. I hate food shopping 