The petition set up by campaigning group 38 Degrees has attracted more than 44,000 signatures since Thursday (9 August).
"Dear Google. It's time for Google to pay its fair share of tax. There's nothing responsible about only paying £6 million in UK tax on hundreds of millions of pounds of revenue.
"Please do the right thing," the petition states.
However, Google has said that .
Google has based its international operations in the Irish Republic, where the corporation tax rate is 12.5 percent, compared to the main rate of corporation tax in the UK of 24 percent.
It also channels money via another subsidiary registered in the tax haven of Bermuda, as another way of legally avoiding paying tax.
However, a member of the Treasury Select Committee believes that Google could be called in to explain its tax practices to MPs.
"It is entirely immoral, this is a company avoiding its obligations and we are letting them get away with doing it," John Mann told the Independent.
"I think it would be highly appropriate to pull a Google executive in front of the committee to justify their failure to pay proper taxes. We would be looking at covering the issue in this parliamentary session, so before Easter, realistically.
He added: "Whether it is illegal or immoral, the British tax payer loses out. Google is one of the big ones, but there are others."Google reported overall losses of £24.1 million in the UK, where it set aside a £51.4 million charge for share awards to its employees.
It was revealed last year that Google's UK practice had paid just £935,000, or 0.4 percent, of tax on revenues of £239 million.
In the six years leading up to the end of 2010, Google paid a total of £8 million of corporation tax in the UK.
Eric Schmidt, Google's executive chairman, has previously said: "We could pay more tax, but we would have to do so voluntarily."