Meanwhile, Asda came bottom of the survey, scoring just 62 per cent in the survey - compared with 74 per cent for Waitrose, and 72 per cent for both Aldi and Lidl.
However, when it comes to online shopping, it's one of the UK's smaller grocers that clinched the top spot.
Iceland got a customer store of 77 per cent from online shoppers, thanks to its "great value for money and convenient delivery slots", said Which?.
"Our survey found that it’s the substitution rating and value for money that really make an online grocer stand out – customers want great deals and to receive exactly what they ordered," it added.
But when it comes to convenience, it turns out the nation's heart belongs to M&S Simply Food, which was given a customer score of 75 per cent.
Little Waitrose followed close behind, with 66 per cent, while Best-One, which only has 60 stores in the UK, came third, with 64 per cent.
"With concerns over rising prices the competition among supermarkets is fiercer than ever," said Richard Headland, editor of Which? magazine.
"While value for money remains a top priority, in-store appearance and the availability of quality and fresh products can also go a long way to satisfying shoppers’ needs."
Figures published by Kantar earlier this month showed Waitrose's market share had edged up to 5.3 per cent in the 12 weeks to the end of January, with sales rising 3.4 per cent. Tesco remained the largest supermarket, although its market share fell to 28.1 per cent.
Read more: End of days: Waitrose is closing stores