Online retail sales in Europe are seen doubling by 2018 to €323 billion, with Amazon.com expected to grow even faster than that, market research firm Mintel said.
In a survey of 19 markets in Europe, Mintel predicted that online sales would grow to €188 billion in 2013 from €166 billion in 2012.
Mintel said Germany, Britain and France would remain by far the biggest markets for online retail by 2018.
However the Netherlands, Spain and Poland should grow at a faster rate and Norway and Sweden have the highest online per-capita spend.
"There is a big North-South divide in e-commerce in Europe," said Mintel European retail analyst John Mercer, noting French participation levels lag Britain and Germany by five years and Spain, Greece, Portugal and Italy are even further behind.
Mintel said Amazon is extending its lead on the continent, growing market share to 9.8% in 2012 from 9.2% in 2011, while Germany's Otto, its next closest rival, saw its share slip to 3.3% from 3.9%.
Mintel predicted Amazon could double its Europe-wide market share in the next three to four years despite negative publicity in Britain over its low tax bills and in Germany prompted by strikes at its distribution centres.
Mercer said Amazon was performing strongly despite having only five dedicated country websites in Europe - in Britain, Germany, France, Spain and Italy.
"Italy is a tiny market. Perhaps it would be more worthwhile to have launched dedicated sites for the Nordics," he said. "In terms of spend per capita, the Nordics are much higher."
Mintel said it would still be 2021 before Amazon overtook Germany's Schwarz group, owner of Lidl discount stores, as Europe's biggest retailer, assuming current trends continue.
Amazon last month forecast disappointing income and revenue as it grapples with a weaker international market, overshadowing improving profitability and economic conditions in the United States.
British grocers are also well represented in Mintel's European top 10, with Tesco holding its market share steady at 2.3% and Walmart-owned Asda and Sainsbury on 1.1% and 0.9% respectively, reflecting the popularity of online grocery shopping in Britain.
"In mainland Europe, online shopping is largely non-grocery," Mercer said. "That is not going to change fast."
The Mintel report said Britain and France have the strongest demand for buying online and collecting in-store, a trend yet to take off for Germans, who prefer their goods to be delivered.