The latest figures from TNS Worldpanel show that Tesco had increased its share from 30.3 per cent in the same period last year to 31.4 per cent.
Meanwhile, Asda had widened its lead over Sainsbury's to 0.9 per cent with 16.6 per cent in the 12 weeks to October 8.
TNS Worldpanel director of research Edward Garner said that the figures confirmed that the market 'remains competitive' and would make interesting reading for the 'ongoing competition investigation' into British supermarkets.
The study also revealed that overall expenditure had risen 5.4 per cent to£17.8 billion in the 12 weeks to October 8 compared with the same period last year.
Garner said that turnover at Morrison's continued to grow, but that if the business was to 'show future increases' it would need to repeat its success in its Yorkshire heartland. Morrison's market share has remained close to 11 per cent for the past 16 periods.
TNS added that at 3.9 per cent - up from 3.7 per cent a year ago - Waitrose now held a record market share.