Office for National Statistics estimates suggest that volume retail sales in July were up 4.2% on the corresponding month last year.
Growth of 0.5% in the last quarter means stores have enjoyed the longest period of sustained growth since record began in 1996, the ONS said.
The value of online sales increased by 13% over the year and now accounts for 12.6% of all retail sales.
Price deflation meant that total retail sales in July were only up by 1% in value on the same month in 2014.
The "predominantly food stores" category in the ONS figures - which includes sales of alcohol - saw volumes lagging behind the retail industry as whole, up 1.3% over the year. Average store prices were down 2.2% to result in an overall drop of 0.8% in sales value.