Overall shop prices were 1.7% lower in October than the same time last year, almost unchanged from the 1.8% recorded in September, the BRC-Nielsen Shop Price Index shows.
Deflation on non-food items remained unchanged at 2.1% for the second consecutive month, coming in significantly higher than food deflation of 1.2%, a slowing from September's 1.3%.
The figures show a marked divergence between ambient and fresh food deflation, with fresh food prices 2% lower than in October last year while ambient prices were just 0.2% lower.
The report predicts shop price deflation will move closer to zero at the turn of the year and "could even move into inflationary territory" at some point during the first half of next year.
British Retail Consortium chief executive Helen Dickinson said: "While we know that the devaluation of sterling since the Brexit vote is stoking inflationary pressures, the good news for consumers is that retailers have been successful in managing this to date and there is still no impact visible in shop prices.
"However, it is inevitable that imported inflation will begin to make its mark and we would expect to start to see this effect coming through in the first quarter of 2017."
Nielsen head of retailer and business insight, Mike Watkins, said: "Supermarkets are keeping prices low and inflationary pressure in the supply chain is not yet being passed on, as competition for the wallet of the shopper continues to be intense.
"Fresh food is a key battle ground for attracting new shoppers and there have been further price cuts in recent months.
"Across the non-food channel it is unseasonably warm weather that is having the biggest impact on sales so retailers are holding prices and making promotions attractive to help encourage visits to store."
Analysts have already warned that there is likely to be a round of price hikes in January as retailers look to pass on higher costs once the festive season is out the way.
Former chief executives of Tesco, Sainsbury's, Asda, Morrisons, Marks & Spencer and B&Q all warned ahead of the EU referendum that a drop in the pound - coupled with supply chain disruption - would cause prices to spike.