Latest grocery share figures from Kantar Worldpanel for the 12 weeks ending 17 August showed grocery price inflation fell for the eleventh consecutive period.
It now stands at just 0.2 per cent, the lowest level for eight years, which is when the company began this specific measure.
Tesco still rules the roost, hogging a 28.8% market share. But this is down 1.4 per cent in a year as rivals catch up.
Asda and Waitrose, for example, performed ahead of the market, with both boosting market share to 17.2 per cent and 4.9 per cent, slightly up on the same period last year.
But with the exception of Asda, the big four are being squeezed: Morrisons', like Tesco's, share remains under pressure, while Sainsbury’s dropped from 16.5 per cent to 16.4 per cent.
Meanwhile, Aldi and Lidl maintained record shares of 4.8 per cent and 3.6 per cent, thanks to 53% of households in Great Britain shopping at either outlet over the past 12 weeks.
Director Edward Garner said: "Competitive pricing among the big grocers and deflation in the price of staple items such as vegetables has driven inflation down yet again.
"This naturally impacts on the overall growth of the grocery market, which has fallen to a 10-year record low of 0.8%."
"Asda and Waitrose have achieved growth with differing strategies: Asda pushed its 'price lock' strategy to keep prices on everyday essential items low.
"Waitrose is running competitive offers on home delivery alongside offers for myWaitrose card users allied to its quality and provenance positioning."