Protesters against corporate tax avoidance plan to target Vodafone and Top Shop outlets in more than 50 towns and cities around Britain tomorrow in the biggest day of action by the UK Uncut group so far.

The action, on traditionally the busiest pre-Christmas high street shopping day, will also be aimed at other stores – but the main focus will be Vodafone and outlets run by Sir Philip Green's Arcadia group.

The protests are organised locally – UK Uncut is a loose alliance of activists with little formal structure – making it hard to gauge the scale of tomorrow's events, but the group's website has a list of more than 50 planned demonstrations around the country.

Most are likely to involve sit-ins of the sort which forced several branches of Vodafone and Top Shop to close briefly a fortnight ago, among them the latter's flagship store on Oxford Circus in central London.

However, the UK Uncut group in Brighton is promising a wider "disruptive tour of Brighton's biggest tax-dodgers" while the plan in Oxford is called the Monaco Tax Dodger Grand Prix – a reference to the tax haven residence of Green's wife, Tina, in whose name the bulk of the family business empire is registered.

The biggest protest is again likely to be in London, where the group aims to emphasise what it says is the link between tax avoidance by corporations and rich individuals and the current round of government spending cuts.

One contingent plans to hold a mock school sports day in the Oxford Circus Top Shop to protest against cuts to sports funding, while Vodafone's nearby flagship outlet will see a silent "read-in" to highlight cuts to libraries.

Daniel Garvin, of UK Uncut, said the group was aware that high streets would be extremely busy. "So far, members of the public have been very supportive, but we don't want to disrupt people too much," he said.

"The London protests will be limited to two hours, and we hope to keep shoppers informed about what's happening."

UK Uncut – which has spread rapidly in a matter of months, mainly through social media such as Facebook and Twitter – claims a clampdown on corporate tax avoidance could bring the government an extra £25bn a year, greatly reducing the need for spending cuts.

Tax protesters claim Vodafone was let off an unpaid tax bill of £6bn, a figure tax authorities described as "an urban myth".

The focus on Top Shop is based around savings made by Tina Green's residency in Monaco, which enabled her to receive a £1.2bn dividend in 2005 tax free. Her husband, who has been advising the government on efficiency savings, insists he pays a proper amount of UK tax.

While corporate tax avoidance strategies are legal, UK Uncut argues that they are immoral in such financially straitened times.

Interviewed by BBC Radio 4's Today programme this morning, Murray Williams, a UK Uncut spokesman, said: "What we're saying, and what people up and down the country are saying, is that that's now socially unacceptable.

"In a time when we're being told that we're all in this together and when we've all got to accept these harsh cuts to housing benefit and the NHS and take a hike in VAT ... trying to claim that these companies then don't have to pay their fair share of that too – I just don't think that's on."

Asked whether the group would be better off putting pressure on the government to change the rules on tax, he said: "I think this is targeting the government.

"Just because we're sat in front of a Top Shop store or in front of a Vodafone store doesn't mean this isn't putting pressure on the government.

"It's making this a big issue. It's highlighting the problem in our tax system that the super-rich often pay proportionally less tax than the poorest people in society, which surely cannot be fair at a time of these massive austerity cuts."

Vodafone refused to say whether it was taking any measures to secure its stores against the protests, while Arcadia had no immediate comment.