I am surprised that Morrisons keeps cropping up, as I think they are quite price, I would put them on the same level as Sainsburies.
Cost wise from cheapest to most expensive:
Asda
tesco
Sainsbury/Morrison
Waitrose
Dh and I did cost comparison one week on everything, and that was what we found.
BUT Asda is about 10% cheaper than Tesco, but Tesco give you clubcard vouchers. If you use these cleverly (doubling points etc) then you probably get more form Tescos over a year.
As to value (which isn't the same as pure cost) I find that you have to get to know your supermarket and shop around a bit. So Smart Price orange juice is foul, so I don't buy it, but smart price tinned chopped tomatoes are fine. That way I can save more, but still eat nice food.
We do our weekly shop in Asda, just for price. I spend £100 ish a week, so at 10% cheaper than Tesco over a year that is £520.
Mind you, our local Asda is absolutely vast and they stock everything, I have yet to find something they don't have.
(actually, not true, they don't have angelica, but then none of the supermarkets sell it any more, not even waitrose
)
I also find that the staff in our Asda are drilled on customer service, so if you ask for anything, they are super helpful