Britain could have financed the Olympic Games out of the VAT it is losing on the sales of digital services, new research shows, heaping more pressure on George Osborne to close tax loopholes enjoyed by multinational companies in Wednesday's autumn statement.

As Britons splashed out millions on Christmas gifts on the busiest online shopping day of the year, a report by a leading telecoms and digital consultancy suggests the UK is losing over €2bn (£1.6bn) a year in VAT on digital services bought by British consumers from suppliers such as Amazon which are based overseas. Greenwich Consulting estimates the UK will lose £10bn between 2008 and 2014. Ministers say the London Games cost taxpayers £9bn.

The chancellor is expected to find more cash in the autumn statement to fund a drive by Her Majesty's Revenue and Customs to raise an additional £10bn in tax revenues. But the revelation that Britain is losing so much revenue through tax loopholes will intensify demands at Westminster and beyond for tougher action on multinationals, such as Google and Starbucks, paying small amounts of tax.

The anti-tax avoidance pressure group Uncut said that it was planning protests in Starbucks cafes this Saturday, involving "creative civil disobedience", and follows stinging criticism of tax avoidance MPs on the public accounts committee who accused the coffee chain, Google and Amazon of "immoral" use of secretive jurisdictions, royalties and complex company structures to avoid paying tax on British profits.

Margaret Hodge, the committee's chair, said she had already stopped buying coffee at Starbucks and ceased using Amazon. "I think actually the government can do things like … we buy a lot of stuff, we can say we won't buy from companies. I think it's good citizenship."

Asked whether David Cameron would back calls for a consumer boycott of firms which avoid tax, the prime minister's official spokesman said: "The issue for government is how we tackle that tax avoidance … What we have to do in government is make sure we are tackling that kind of aggressive tax avoidance. We are doing that in a number of ways. We are bringing in a general anti-avoidance rule, we are working with other countries."

The question of a boycott was "an issue for individuals", said the spokesman.

Sainsbury's chief executive, Justin King, recently urged consumers to vote with their wallets, boycotting those companies that avoid tax. King said: "If you send a clear message as a consumer to any business that you don't think it pays its dues in the UK you can bet your bottom dollar that they'll make a change very quickly."

John Lewis boss, Andy Street, has also criticised the tax avoiders, pointing out that British companies paying corporation tax were at a disadvantage to those that channel their income abroad: "You have got less money to invest if you are giving 27% of your profits to the exchequer than if you are domiciled in a tax haven."

Under the EU's VAT rules, digital supplies to non-business customers – such as ebooks, music downloads and online apps – are classified as services rather than products. VAT on electronic services is imposed at the rate applying to the country in which a company is headquartered rather than the rate applied by the country in which it is bought. Amazon, for example, is based in Luxembourg and therefore charges its customers 3% VAT for ebooks, compared with the 20% levied in the UK.

Charlie Elphicke, a Conservative MP and a former tax lawyer, believes that the EU should accelerate plans to change the way VAT is charged on digital services, which is due to be phased in between 2015 and 2019. "This is yet another example of industrial scale tax avoidance by foreign owned multinational corporations. Their behaviour is irresponsible, unethical and unacceptable," he said.

"Billions of VAT is being lost that is needed to fund schools and hospitals or cut the deficit. I welcome the action that has been taken by the government so far – yet we need urgently to close this loophole and enable British businesses to compete on a level playing field."

The Greenwich report was commissioned by Philippe Marini, chairman of the French senate's finance committee and was prepared for a private meeting of pan-European politicians, civil servants and tax specialists in Brussels. Marini supports an earlier date for bringing into line with other goods the rules for charging EU VAT on digital services.

"At the European level we need to renegotiate the schedule for implementing the VAT directive on electronic services in order to bring its application deadline nearer than 2015 or 2019, the term of the transition phase," Marini said.

An HMRC spokesman said: "It is a natural consequence of the VAT rules rather than any lack of compliance that a business in say, Germany, supplying such services to UK customers will account for VAT in Germany and not in the UK.

"Businesses have the freedom to establish themselves in whichever member state they wish. However, some UK businesses claimed to have moved their operations to other member states in order to benefit from lower VAT rates where in reality the supplies were still made from the UK. HMRC has successfully challenged such arrangements."

Richard Asquith, an indirect tax specialist and head of VAT at TMF, the international compliance consultancy group, believes the €2bn a year loss may be a conservative estimate. "What they may not be figuring in is sales of computer games and apps over the internet from outside of the EU. Many non-EU traders simply ignore EU VAT since it is close to impossible to track down."

The crucial business to consumer (B2C) market in Europe for electronic business services was worth €124bn in 2009, according to Greenwich. The UK was by far the biggest market, accounting for over one third of total sales.

The wider internet economy contributed £121bn to the British economy in 2010 according to a report by The Boston Consulting Group. The report, published earlier this year, said the UK's internet economy is growing at a rate of 10.9%, and is expected to be contributing £225 billion to the overall economy by 2016.

But the Greenwich report says the UK was the least successful country at converting B2C sales into tax revenue. Based on the highest estimates, its combined VAT and corporation tax income from B2C business was generated at a rate of 15% of total sales.

France and Germany secured conversion rates of 19% and 21% respectively while Benelux countries converted 50% of their €3bn B2C trade into tax revenue.

Marini is a longstanding campaigner for fair and neutral taxation of the digital economy. He has drafted a law to allow the French government to capture a greater proportion of revenues generated by the sale of digital services.

François Hollande's government says it will look at proposals next year which will restrict the ability of online companies to pay taxes on revenues earned in France in European countries with lower tax rates.

Marini is trying to encourage a pan-European response to the imbalance between sales revenue generated in a particular economy and the taxation generated for the host country. While the UK is the biggest loser from lost VAT revenues, France, Germany, Spain and Italy are also identified by the report as countries suffering from diversion of VAT to other countries.

• This article was amended on 4 December 2012 to remove repetition in the final paragraph.