Campaigner Ed Brompton said: "This money - £6bn - could be spent on schools, housing and hospitals".
But a Vodafone spokesman denied the tax bill reports, adding: "We pay our taxes in the UK and all of the other countries in which we operate".
A spokesman for HM Revenue and Customs said of the £6bn: "That number is an urban myth".
Four shops in central London were forced to close on Saturday because of the demonstrations, sparked by a campaign on Twitter and Facebook.
Other shops were closed by demos in Brighton, Bristol, Edinburgh, Glasgow, Hastings, Liverpool, Manchester, Oxford and York.
One of the protesters, Deborah Lee, said: "The cuts are not fair; we're not all in this together, and there are alternatives. Why not start by collecting the tens of billions owed in taxes by wealthy corporations? The government is writing off the taxes from big business while treating normal people on benefits like criminals".
Another protester, Ben Olabayi, said: "We will not pay for their crisis! The public need to join together and hit the streets to take concerted action to fight these cuts".
BBC News
