Campaigners against tax avoidance by big business forced Topshop's flagship store to close temporarily as they took action in 21 towns and cities.
They blew whistles and chanted at the Oxford Street store, while in Brighton some glued their hands to windows.
Topshop boss Sir Philip Green's wife, the firm's direct owner, has been criticised for living in a tax haven.
UK Uncut says Topshop's parent firm Arcadia was its main target. Nobody from either company has commented.
Protest organiser UK Uncut said it also targeting Boots, HSBC, Barclays and Vodafone.
Campaigners were forcibly removed from the Oxford Street branch by private security guards and police.
In Birmingham, a protest at Topshop's store in the Bullring lasted 30 minutes, before campaigners were ejected by security guards.
In Brighton, where police made 18 arrests, eight demonstrators superglued themselves to the inside of the shop's windows.
Sussex Police say they were all arrested for criminal damage and aggravated trespass, plus one for assault.
Nine others were arrested outside for public order offences, and one for possession of a bladed article, police added.
Meanwhile, some 30 protesters also targeted a Vodafone store and a Topshop in Oxford, UK Uncut said.
Smaller-scale protests were staged in Glasgow, Edinburgh, Liverpool, Leicester, York, Bristol, Portsmouth, Southampton and Cambridge.
Activist Benjamin Neem, 30, said: "Philip Green is a multi-billionaire tax avoider, and yet is regarded by David Cameron as an appropriate man to advise the government on austerity.
"His missing millions need to be reclaimed and invested into public services, not into his wife's bank account."
Rebecca Davies, 32, said reclaiming unpaid tax was an alternative to the government's planned cuts.
"The tax gap in the UK is an estimated £120bn, £25bn of this down to tax avoidance by extremely wealthy individuals and big business, while the government is barely lifting a finger to stop it," she said.
But one female shopper in London, who asked not to be named, said: "I don't care what they are protesting about. They purposely picked this weekend to cause as much inconvenience as possible.
"People are desperately trying to do Christmas shopping. This is my only free weekend and I can't go to the one place I wanted to."
Topshop owner Sir Philip is one of the UK's most successful retailers.
With a personal fortune of more than £4bn, he owns the Arcadia Group, whose fashion chains include Topshop, Burton, Dorothy Perkins, Evans and Miss Selfridge.
His wife Tina is the direct owner of Arcadia, and she is officially a resident of Monaco. This enabled her to gain a tax-free £1.2bn dividend in 2005.
Speaking in August about the tax status of his wife, Sir Philip told the BBC: "My wife's not a tax exile - my family do not live in the United Kingdom, it's somewhat different.
"We do pay all our tax in Britain. I think we have paid over the last five years some £300-400m in taxes on profits that have been made on our company.
"I'm a UK taxpayer, I work here every week, we employ 45,000 people in the UK and we have got a £500m payroll."
Earlier this year, Sir Philip was appointed by the government to look into Whitehall efficiency and he produced a report which described "staggering" wastage.
Saturday's action follows similar protests in October when UK Uncut picketed entrances to Vodafone, which has also been accused of avoiding tax payments.