The data showed a record £469m was spent on premium own label lines in December, with chilled items, fresh meat and bakery featuring prominently.
Both retailers increased their sales by 16.8% compared with the same period the previous year, taking Aldi's share of the entire United Kingdom grocery market to 6.8% from 6% a year earlier and Lidl's to 5% from 4.4%, Kantar Worldpanel said.
"Shoppers parted with £747m on 22 December alone, making the Friday before Christmas the busiest shopping day ever recorded".
Total grocery spending in the United Kingdom during the four weeks to 30 December hit £10.5bn, up 3.7 per cent year-on-year.
"Shoppers are splashing out despite fewer promotions to tempt them".
That is the lowest level of promotional activity at Christmas since 2009.
Like-for-like prices rose by 3.7% in the 12 weeks, a slight increase on the 3.6% rise reported last month.
However, market share growth at Aldi and Lidl continued to outpace the Big 4, with the German discounters both recording sales rises of 16.8 per cent. The combined market share of the two German supermarkets stood at 11.8%, up from 10.4% a year earlier, attracting almost one million additional households during the period, Kantar added.
Mince pie sales rose by 13.2% year-on-year and alcohol sales grew by 5.1% year-on-year, with spirits up 7.6% as consumers favoured gin and whisky.
The Co-op was the only grocer to have recorded a decline in sales, with a 0.2 per cent drop, and its market share also dipped 0.1 per cent to 5.2 per cent.
Kantar said that this was the fastest sales growth the retailer has seen since June, helped by a 6.4 per cent increase in sales of standard Tesco own label. According to Kantar, the fact that Christmas Day fell on a Monday this year helped boost Tesco Express, as larger supermarkets were forced to comply with restricted Sunday opening hours.
In terms of market share, Tesco held on to a 27.5 per cent portion in the 12 weeks to 31 December, the same share it claimed in the same period of 2016. Excluding the discounters, sales were up 2.3 per cent.
Figures from the BRC also out on Tuesday showed United Kingdom retailers saw a 0.6% like-for-like sales rise in December but the report highlighted how the "severe pressure" on spending was weighing heavily on some firms much more than others.
According to figures from the British Retail Consortium, food sales for the three months to December rose 4.2%, their biggest rise in six months. This compares to sales growth for the big four United Kingdom supermarkets of 3.1% for Tesco PLC, 2.0% for J Sainsbury PLC, 2.1% for WM Morrison Supermarkets PLC, and 2.2% for Asda, part of Wal-Mart Stores Inc.