Lawmakers said a Reuters report that showed Starbucks had been telling investors its British unit was highly profitable while telling authorities the unit was loss-making, and thereby not liable for tax, undermined public trust in the tax system.
The Seattle-based group, with a market capitalization of $40 billion, is the second-largest restaurant or cafe chain globally after McDonald's.
Margaret Hodge, chair of the Public Accounts Committee and a member of parliament for the centre-left opposition Labour party, is among several lawmakers who said they wanted Her Majesty's Revenue and Customs (HMRC), the tax authority, to launch an investigation into the company's tax affairs.
Hodge said the head of HMRC and other officials would be testifying to the committee, whose duty it is to see the government gets value for money in its financial affairs, next month and that HMRC had "questions to answer" about the practices of Starbucks.
None of the lawmakers suggested Starbucks had been engaged in any kind of wrongdoing and the company said it paid its tax in Britain to the letter of the law.
The Treasury Subcommittee, which oversees HMRC, is also due to question HMRC officials and its chairman, lawmaker George Mudie, said he planned to question them about Starbucks.
He said he also hoped the committee could hear from executives from the company, although he noted he would need broader committee support to call them to testify.
Labour member of parliament John Mann, who sits on the subcommittee, said he would like it to hold an investigation focusing on Starbucks but Mudie said this was unlikely.
HMRC does not comment on individual taxpayers and rejected any challenge to its efficacy.
"We make sure that multinationals pay the right tax to the UK in accordance with UK tax law," it said in a statement.
Steve Baker, a member of parliament for the centre-right Conservative party that rules in coalition, also called for an inquiry.
"I am a highly free-market person but what I want is simple transparent tax law that is actually obeyed ... there are some serious questions to answer here," he said.
"LETTER OF THE LAW"
Taxpayer confidentiality means HMRC would not be able to confirm a probe if it launched one.
Baker and Hodge said the government could get around this, and reassure the public the matter was not being ignored, by confirming in parliament that an HMRC probe was taking place.
Labour member of parliament Michael Meacher said he planned to table a motion asking the government to launch its own investigation into Starbucks and potentially other big companies that are paying minimal taxes on big British revenues.
The legislators said such investigations should also lead to recommendations on how to change tax law to prevent companies from shifting profits overseas.
Kris Engskov, managing director of Starbucks Coffee UK, told Sky News television that HMRC had not contacted the company to say it was under investigation. He added that Starbucks had no plans to change its UK accounting practices.
In a blog on the company's website, he said: "Starbucks pays and will continue to pay our share of taxes in the UK to the letter of the law."
He went on to note the contribution Starbucks makes to the British economy as an employer and as a customer for farmers and cake makers.
Unions said the Reuters story on Starbucks showed the government needed to do more to close loopholes that allowed companies to avoid taxes.
"Hardworking families are being forced to pay off the deficit while companies like Starbucks laugh all the way to the bank," Len McCluskey, General-Secretary of Unite, Britain's largest union, said.
The Northern Ireland Committee of the Irish Congress of Trade Unions called for a boycott of the cafe chain, a call echoed by some members of parliament.
"Support local cafes and bars, and send Starbucks and other tax dodgers a clear message - Unless you contribute to society, this society has no cash for your coffee," ICTU Assistant General-Secretary Peter Bunting said.
(Additional reporting by Alessandra Rizzo; Editing by Michael Roddy)
By Tom Bergin