June saw a 17% increase in online sales compared with the same time last year, building on an "extremely strong" May when retailers recorded their highest year-on-year growth rate in 11 months, according to the IMRG Capgemini eRetail Sales Index.
Clothing performed strongly but the rain-soaked month meant sales of beer, wine and spirits tumbled by 7% as consumers put off summer barbecues, and health and beauty sales also fell by 5%.
The index also shows that growth in sales via tablet devices nosedived to a year-on-year 0.4%, the lowest figure since monitoring began in 2013.
Conversely, sales on smartphones grew 69% on this time last year.
The average basket value of goods bought online was also up, from £75.11 in June last year to £80.34.
Tina Spooner, chief information officer at IMRG, said: "While the index results reveal a strong performance during June, it is too early to say whether the Brexit vote will have any long-term impact on the UK's online retail sector.
"However, early signs from a recent IMRG poll of retailers found that around two-thirds of online merchants saw a slowdown in sales in the few days after the EU referendum, with most reporting sales appearing to recover to normal levels again afterwards."
Capgemini management consultant Bhavesh Unadkat said: "It's widely agreed that consumer confidence is falling, and this is something that is being heard from retailers across a myriad of sectors.
"As a result it's great to see that, both in the run-up to the referendum and in the immediate aftermath, online sales growth remained strong.
"These figures obviously don't encapsulate the entire Brexit fallout, and the full impact of the referendum is something that we will not be able to wholly analyse for a number of months. In the meantime, retailers need to continue to focus on ensuring they give their customers every reason to shop with them."
Earlier this month a one-off GfK survey found consumer confidence had seen its sharpest drop in more than 20 years since the Brexit vote, with a third of shoppers believing prices will increase rapidly in the next year.