The latest till-roll figures from Kantar Worldpanel showed Tesco's sales fell 3.8 per cent in the 12 weeks ended July 20.
That was the steepest decline since the researchers began comparable records in 1994, as the chain's market share fell to 28.9 per cent from 30.3 per cent a year ago.
Big four rival Morrisons also saw its sales fall 3.8 per cent in the 12 weeks, leading its market share to slip to 11 per cent from 11.5 per cent, as low industry inflation kept sector growth to a 10-year low.
But fast growing discount supermarkets Aldi and Lidl made record sales as price competition in the sector weighed heaviest on the country's big four players.
Sales at German discounter Aldi rocketed 32 per cent over the year, taking its market share to a record 4.8 per cent, just behind the upmarket Waitrose, which is part of the John Lewis Partnership.
Rival low cost business Lidl, which also has its roots in Germany, saw its sales leap 19.5 per cent, which kept the firm's market share at its record level of 3.6 per cent.
Sainsbury's sales grew 1.2 per cent to maintain its market share at 16.6 per cent, while Asda grew 0.9 per cent, which kept its market share at 17 per cent.
Frozen food retailer Iceland saw its sales dip 0.3 per cent over the period, its first fall since 2005, though its market share remained at two per cent.
The Kantar data also showed that grocery price inflation fell for the tenth quarter in a row to 0.4 per cent, due to price competition and the deflation of staples such as vegetables, milk and bread.
Inflation in the sector is at its lowest level since October 2006.
Low levels of inflation left industry growth at just 0.9 per cent, the lowest level for a decade.
Last week Tesco ousted chief executive Phil Clarke and announced its second profit warning in two years after it said trading was "more challenging than we anticipated".