While the frozen-foods specialist topped the online list, Co-op shops ranked worst for in-store satisfaction - for the third year in a row.
Waitrose was number one for its physical stores for the second year running in the annual Which? supermarket survey, scoring a customer satisfaction rating of 75 per cent.
The upmarket chain fared well for the quality of its own label products, staff helpfulness and store appearance.
But Co-op, scoring 57 per cent, frustrated consumers for failing to have products in stock, being poor value for money and having a small range of products.
A spokeswoman for Co-op described the survey as “backward-looking” and insisted service has improved.
She said: “This backward looking survey does not reflect the massive strides we have taken recently.
“Our prices are lower, our produce is fresher and our products more exciting than they have ever been, and that’s why the latest market share data out last week showed Co-op as the fastest-growing and most frequently visited supermarket.”
Tesco, the UK’s largest retailer, came second from last, disappointing shoppers with stock availability and staff helpfulness.
The poll of 7,009 shoppers, carried out in November, showed Asda as having the worst online service, with customers scoring it 65 per cent.
This was contrasted with Iceland’s service, which was awarded a rating of 77 per cent for offering the best value for money as well as a high-quality own-brand products.