IMRG chief executive James Roper said: 'We won't have hard data until January 15, but we believe that we will see 45 per cent or even 50 per cent growth for December.'
That would push online spending in the 10-week run-up to Christmas to£7.5 billion,£500 million more than the IMRG was expecting.
Online sales at Tesco soared by more than 30 per cent during the four-week period to Christmas, as 1.3 million shoppers ordered groceries and gifts online. During the Christmas week, Tesco customers ordered 14 million grocery items over the internet, including 11,000 turkeys.
Online sales of mince pies were up 20 per cent on last year and Tesco Wine Club delivered 80,000 orders in time for Christmas, up 50 per cent on the same period last year.
Amazon.com said its worldwide festive sales set a record this year, buoyed by demand for Sony's PlayStation and Microsoft's Xbox. The online retailer's busiest day was December 11 when more than 4 million items were ordered.
On the high street, according to research firm SPSL, shopper numbers on December 27 - the first proper day of the Sales - were up 3.9 per cent on the previous year, making it the busiest Sales shopping day for four years.
Shopper numbers were also 10.1 per cent higher than December 16, which was the busiest pre-Christmas shopping day.
SPSL director of knowledge management Dr Tim Denison said: 'This year has been a difficult one to predict, but the reality is it hasn't been a desperately bad Christmas. What will be fascinating, once we are into the full swing of the Sales, is whether consumers are convinced that the after-Christmas Sales are much different from many of the events, secret Sales and special offers they received pre-Christmas.'
Seymour Pierce analyst Richard Ratner - who forecast the worst retail Christmas in 25 years - said: 'We think Christmas will have been OK, but the question is at what margin?'
A clearer picture of festive trading will emerge at the end of next week when 10 of the UK's largest retail groups - including Marks & Spencer and Sainsbury's - unveil trading updates.
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