UK retailers are under growing pressure as rising energy, transport and supply chain costs increase financial strain.
Total online retail sales of goods and services increased 6.6% compared to the same period a year before.
The group, which includes Marks & Spencer, Primark and Argos, argue the current customs regime gives online rivals such as Temu an unfair edge.
The figure marks the first time online channels have crossed the 60% threshold since the Ministry of Trade, Industry and Energy began its monthly retail survey in June 2016.