Retailer Topshop's flagship branch in London's Oxford Street was one of a series of shops that fell victim to the co-ordinated protest.
A Sussex Police spokesman said 18 people were arrested during a demonstration in Brighton.
He said that eight demonstrators gained entry to Topshop in Western Road and glued their hands to the inside of the shop windows.
A shop worker was assaulted during the demonstration, he said.
Smaller-scale protests were held in 19 towns and cities - including Liverpool, Glasgow, Edinburgh, Leicester, York, Bristol, Portsmouth, Southampton and Cambridge.
The West End protest started at 11am when campaigners from UK Uncut joined together inside Topshop and started blowing whistles and chanting as the store was packed with Christmas shoppers.
Many campaigners were forcibly removed from the premises by private security guards and police.
One campaigner, who wished to be known only as Lucy, said: "I am a peaceful protester. A woman was being thrown out of the store and I objected so I was picked up by two private security men.
"They lifted me by my ankles and my hair. It was quite scary really."
Security guards also removed journalists from the store. One female reporter was carried out by her arms and legs.
A UK Uncut spokesman said they targeted the shop because it was part of Sir Philip Green's Arcadia retail group.
Campaigner Stephen Trevelian, 26, from Brighton, 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."
The activists said demonstrations were also planned against big business outlets around Britain.
The spokeswoman said: "Tax avoidance is a big issue and we believe this is the alternative to the cuts the Government are making."
She said Arcadia stores - which include Topshop, Dorothy Perkins and Miss Selfridge - were the main targets along with Boots, HSBC, Barclays and Vodafone.
The group also criticised the coalition Government's decision to seek Sir Philip's advice on efficiency cuts in the Civil Service.
He produced a report in October which described "staggering" wastage in Whitehall spending.
Activist Bridget Chapman, 39, from Lambeth, south-east London, said: "If people like Philip Green paid their taxes we would not have to make public spending cuts.
"It is outrageous the Government is looking for help from someone like him."
Rebecca Davies, 32, added: "The tax gap in the UK is an estimated 120 billion, 25 billion of this down to tax avoidance by extremely wealthy individuals and big business. The Government is barely lifting a finger to stop it."
The UK Uncut spokeswoman estimated 200 people took part in the London protest.
Around 30 police officers were guarding the door of the store with an even larger number of private security guards.
Christmas shopper Kirsty Lamb, 20, from Camden, north London, said: "I just want to get inside. I think they are being unfair to other shoppers. It's not very festive of them."
Another female shopper, who did not wish to be named, added: "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."
Protesters left the flagship store after about 30 minutes before they tried to move on to neighbouring Miss Selfridge, which is also part of the retail group, but it was closed.
They then marched down to BHS, also owned by Sir Philip, shouting: "Philip Green, pay your tax, it's our money and we want it back."
Once outside the store, which was also temporarily closed to customers, they shouted: "If you want to sell your products, pay your tax."
Causing traffic to stop, they moved on to Dorothy Perkins, also part of Arcadia, but the shutters of the store were already down.
They then entered a Boots branch, singing loudly. After they left, workers promptly closed the shutters, trapping about a dozen shoppers inside.
After the crowd dispersed, the customers were released but the shop then closed again.
The campaigners went on to Oxford Street's Vodafone shop, which was also shut to customers.
Protesters then returned to Topshop and staged a sit-in protest blockading the main entrance. At 2pm the store opened its doors again.
A Scotland Yard spokesman said the protest finished at 4pm.
A spokesman for the Brighton UK Uncut movement said about 50 protesters attended the event and were guarded by 70 police officers.
A spokesman for Sussex Police said that the eight protesters who glued themselves to the windows were arrested for criminal damage and aggravated trespass. Another activist was arrested for assault on a member of the shop's staff.
Nine other people were arrested outside for public order offences, with one campaigner arrested for possession of a bladed article, the spokesman said.
Chief Superintendent Paul Morrison said: "Despite the inclement weather, a number of protesters gathered in the Western Road area of Brighton and attempted to disrupt businesses, including Topshop.
"While we were quite happy to facilitate their right to peaceful protest, a hard core of protesters abused this right and entered Topshop, assaulting a member of staff in the process."
In Oxford, around 30 protesters targeted a Vodafone store and a Topshop which were both forced to shut, a UK Uncut spokesman said.
He said Vodafone shops in Nottingham, Manchester and Newcastle also closed their doors to customers after protests.
In Birmingham, a Topshop store was closed, the spokesman added.
Arcadia group declined to comment on the protests.
Today's protests follow action taken against Vodafone in October, when UK Uncut picketed entrances to its stores.