The latest data from Kantar Worldpanel shows that supermarket sales rose 3.6 per cent during the 12 weeks to September 10. This is the sixth consecutive month in which sales have increased by more than 3 per cent and two thirds of consumers are now shopping at Aldi or Lidl as price increases hit their pocket.
Kantar said that Bradford-based Morrisons has seen a 38 per cent increase in sales of its premium "The Best" line, making it the fastest growing premium range.
Fraser McKevitt, head of retail and consumer insight at Kantar Worldpanel, said: "Morrisons are doing very well with 'The Best'.
"They are also seeing strong sales of alcohol and fresh foods. People are drinking less but drinking better, with strong sales of prosecco, gin and craft ale."
He added that Morrisons is also enjoying good online growth as it catches up with rivals which launched their online offering years before Morrisons did.
Leeds-based Asda attracted an additional 482,000 shoppers – the fastest new shopper acquisition by the retailer in over three years.
“Average spend at Asda is £25.74 – the highest of any grocer – which reflects the success of its larger stores and their appeal for families," said Mr McKevitt.
"Asda has steadied the ship and it's not declining in sales any more."
Kantar said people are feeling pressure on their budgets.
"Inflation is costing an extra £100 a year," said Mr McKevitt.
"People are shopping at the discounters and buying own-label as opposed to brands. Lidl and Aldi are opening a lot more stores, but they are putting a lot of thought and effort into their products. They are not just cheaper. Lidl is doing particularly well in chilled fresh foods like salad."
He said that inflation is expected to come down as the one off hit after the EU referendum starts to work through the system.
"The average British household spends almost £4,200 in the grocers each year so a fall in inflation, which we expect to see as we approach the end of the year, will be a welcome relief," said Mr McKevitt.
"But we don't know about political instability. Who knows what will happen with politics. Shoppers care deeply about Brexit. It's their top worry about the economy."
However he said that supermarkets are in a good position as whatever happens with Brexit, people have to buy food. A number of big ticket retailers such as Doncaster-based DFS Furniture have suffered from falling expenditure as people can postpone buying a new sofa.
Lidl emerged as the UK's fastest growing supermarket with a record market share of 5.3 per cent.
Lidl and Aldi now account for almost £1 in every £8 spent in Britain's supermarkets, up from £1 in £25 a decade ago.
Lidl was the fastest growing supermarket with a sales increase of 19.2 per cent, while Aldi's growth of 15.6 per cent took its market share to 6.9 per cent.
Tesco's recovery continued with sales up 2.7 per cent, although its market share was squeezed by 0.3 percentage points to 27.8 per cent, while Sainsbury's market share fell 0.2 percentage points to 15.7 per cent.
Sainsbury’s sales rose 2.1 per cent, Asda rose 1.5 per cent and Morrisons was up 2.3 per cent, Kantar said.
Food inflation was 3.2 per cent, compared with 3.3 per cent in the previous period.
Poor weather in August hit sales of traditional summer items, with prepared salads seeing a 6 per cent dip and sun care down 16 per cent.
In contrast, consumers spent almost £4m on cold treatments in August, an increase of almost £2m on the same month last year.