Lidl’s sales grew by 16% in the 12 weeks ended 13 September, with Kantar crediting the success of its latest marketing campaign for strengthening the brand.
Online supermarkets will be watching closely to see when Amazon Fresh will launch in the UK and whether it will steal market share
Over the period, 56% of British households visited Aldi or Lidl, according to the data.
Sainsbury's, which is running a "twist your favourite" recipes campaign, outpaced the rest of the big four with sales up a marginal 0.9%.
Fraser McKevitt, head of retail and consumer insight at Kantar said: "With shoppers moving their custom away from the traditional, larger-size supermarket stores, online sales are continuing to boom and are up by 12% compared with a year ago.
"Almost 7% of grocery sales are currently purchased through the Internet and existing online supermarkets will be watching closely to see when Amazon Fresh will launch in the UK and whether it will steal market share or grow the online market even further."
Iceland also saw a boost from its frozen campaign, with sales up 3.4%. Waitrose also saw a relatively strong performance with sales up 2.9%.
Similar data released today from Nielsen indicated that the discounters' would steal more of the UK Christmas market this year than ever before as they become "a bigger part of shoppers’ Christmas repertoire."