They are unlikely to have a bigger/better selection than the in-resort Coop that the OP mentioned is open till 6pm on Sunday, nor be somewhere they can do a big shop. To help the OP’s expectations: I’ve never seen one anything like as well stocked as the Waitrose/M&S Simply Food stores you get at some UK service stations.
I'll be interested to know how it goes on the Eurotunnel. I'll be heading to the UK next month.
Coop open on Sundays? Where would that be?
Many places. Interlaken, for example, has two open on Sundays.