The cost of our secret 100-item shopping basket has dropped by just 0.1% since 8 January. In the previous survey, the GPI fell 1.3% as January price promotions kicked in.
The cheapest retailer was Asda, at £175.96, followed by Tesco at £176.15 then Sainsbury's at £179.62, with Morrisons the most expensive at £180.77.
Tesco's basket fell most in price, by £2.76.
Sainsbury's and Asda have knocked 16p off and 10p respectively off their baskets over the past four weeks. However, Morrisons went against the grain and added £4.77 to its basket.
"I suspect Tesco and Asda just don't see the point of cutting prices further as the market seems to be moving towards value-added," said Freddie George, analyst at Williams de Broë.