Yeah, if you're looking to save money on the bill if you move back to the UK, Jim, Asda or one of the discount chains (Lidl, Aldi, Netto, Iceland) will probably be cheapest. It doesn't always mean they are a good value or the conscientious choice.
Waitrose is expensive, but some of their items are better value. Like their own brand hand soap hands down is the best value at 99p (and very lush). Their essentials line is also the best of the "value" lines of all the shops, IMO. Co-op is second, in my experience, but has good offers soemtimes. Sainsbury's follows in pricing usually. Their basics is hit and miss as are their regular own brand. Their "Taste the Difference" line usually is excellent and is still usually cheaper than the premium brands. Then Morrisons (which aren't always in the city centres, at least in the south). Then Tesco. I didn't list Marks and Sparks as it's not really realistic for most people to shop there exclusively.
Another thing to consider if you're moving back is delivery. There are places that deliver meat, dairy, and produce. Some companies do all three. They have schemes that regularly send you a box, or you can sometimes do a one off order. Then many of the major shops deliver, but it depends on your area. This can be complicated or easy depending on the shop and your computer ability.
IMO, the absolute most expensive way to shop is how my MiL does it when she is low on funds. If she has less than a tenner or only needs a couple of things, she shops at the corner shop. Everything is so much more expensive there, but I'd often see pensioners in there obviously doing a full week shop. The nearest full sized grocery shop was a fairish walk from there, and while there is a butcher and deli on near there, there's nothing but Greggs, off licences, Halal shops, and small corner shops in the area. The one near where we used to live was actually half-way decent with a fairly good selection. I've actually been in small chain shops with less selection. But it is so expensive. Of course, if the pensioners had computers, the know-how and bank cards/credit cards, they could order their groceries in, but obviously that wasn't an option for them. Too bad there wasn't a service to help them with that or their shopping.