Close to one in five non-food items was bought online last month, according to the BRC survey.
There was also a 19.2% growth in internet purchases from a year earlier, the fastest increase in four years.
However, UK retail sales in total rose by just 0.4% on a like-for-like basis. The BRC said the figures represented a "respectable overall result".
Retail sales growth is being driven by the click of a mouse, rather than the ring of the tills”
Online trading in general represented 18.6% of total non-food sales for the final month of 2013, an increase from 16.5% a year earlier.
The BRC's director general, Helen Dickinson, said retailers had invested in their websites and improved delivery times, and added that the surge in the popularity and use of smartphones and tablets had also contributed to the rise in online retailing.
She also highlighted multichannel offerings by some retailers as one of the key factors over Christmas."