In the week to 10 September, sales at John Lewis were up 9.1 per cent on the same period last year, reaching £82.7m. Fashion sales did particularly well, up by 6.8 per cent.
Children's clothes were up by 35.1 per cent, and children's shoes sales were up by 94 per cent, as parents prepared to take their children back to school after the summer break.
"This week saw a strong uptick in sales as some of the delayed Back to School demand came through," said Mark Felix, online trade director at John Lewis. "The warmer weather continues to influence sales, with high-tog duvets selling at a lower rate than last year."
At Waitrose, sales were 7.1 per cent higher than the same week last year. The John Lewis Partnership said this was due to promotions and the warm weather.
Loraine Woodhouse, finance director at Waitrose, said: "The warm temperature drove sales of traditional summer products such as barbeque meat, which was up nine per cent, and ice cream, up by 22 per cent.
"Fruit was also popular with melon and frozen fruit seeing significant growth."
This is a continuation of good fortunes for Waitrose, which said recently that rosé wine and gin were selling particularly well in the final week of summer.