Police have been called to supermarkets across the UK amid crowd surges as people hunt for "Black Friday" offers.
Greater Manchester Police appealed for calm after attending seven Tesco shops, at which three men were arrested and a woman was hit by a falling television.
The force said the issues were "totally predictable" and it was "disappointed" by shop security. Tesco said only a "small number" of stores were affected.
Police were called in places including Dundee, Glasgow, Cardiff and London.
Originating in the US, Black Friday is becoming a major UK shopping day.
Visa has predicted that UK shoppers will spend £518m online on cards on Friday - which would make it the country's biggest internet shopping day in history.
Police in Manchester tweeted: "At least two people arrested at #BlackFriday sales events already this morning. Keep calm people!"
The force said there had been "disturbances" at the seven Tesco stores.
Incidents at those stores and other locations included:
- About 200 shoppers refused to leave a store in Middleton "despite being told stock had all gone"
- Fights broke out between shoppers in Stretford, and a woman suffered "minor injuries" after being hit by a falling television. The store was closed at 00:36 GMT
- A man was arrested in Salford after he threatened to "smash a staff member's face in"
- A woman broke her wrist in a crush, with Greater Manchester Police's deputy chief constable Ian Hopkins describing shoppers' behaviour as "appalling"
- In Wigan, officers were called to reports of "several hundred people trying to enter the store". Police added: "Two men were ejected before control was regained"
- There were reports of fighting in a store in Hattersley, where a man was arrested for a public order offence
- A man was arrested for assault at a store in Green End
- Bicester Village shopping outlet in Oxfordshire had to temporarily close after roads around it became gridlocked by Black Friday shoppers
In London, police were called by both Tesco staff and queuing shoppers as people gathered at the Glover Drive store in Edmonton.
Officers also attended Tesco stores in Willesden and Surrey Quays.
The Metropolitan Police said officers worked with staff to "ensure that sale-goers were able to enter and exit the stores safely", and said no-one had been injured "as a result of the overcrowding".
Sgt Paul Marshall, a Metropolitan Police officer, tweeted: "Even on #BlackFriday shoving people to the floor so you can get £20 off a Coffee Maker is still an assault."
In South Wales, police said they were called by concerned staff at a number of Tesco stores.
A spokesman said officers were twice called to Tesco in Excelsior Road, Cardiff, just after midnight, when concerns were raised about customer conduct inside the shop. No arrests were made.
Police were called to Tesco at Silverburn in the Pollok area of Glasgow about 11:45 GMT on Thursday after staff reported scuffles among several customers.
The store was closed for a period, and footage from the scene shows shoppers shoving each other as they attempt to grab items from trolleys.
Police were also called to the Tesco in Kingsway, Dundee, to help with crowd control.
Avon and Somerset Police said they were called after scuffles in the queue at Tesco in Brislington, Bristol, at about midnight.
The BBC's Zoe Conway tweeted a picture of a woman on her knees with the words: "Customers knocked to the ground in the rush at Asda Wembley #BlackFriday."
Jamie Hook was buying food at Tesco in Stretford on Thursday night when he said "the screaming started".
"I looked at the massive crowd to see people climbing over shelves and displays, staff running for cover, fights breaking out, stock flying through air, people breaking through carrying televisions - and this was before the sale had even started," he said.
"The lady on the till I was at was in tears, terrified of it all, but she was under orders to close her till to go and help crowd control."
Ross Lewis was at one of the stores participating in Black Friday in Cardiff. He said people fought to get hold of television sets.
"People were biting each other, pinching, punching, kicking - it was just absolutely horrendous, it was so, so bad."
Sir Peter Fahy, Chief Constable of Greater Manchester Police, expressed his frustration via his Twitter account about the amount of Black Friday-related work being asked of his officers.
In a statement, he also said he was "disappointed that stores did not have sufficient security staff on duty".
"Across Greater Manchester large supermarkets already make significant demands on policing through calls to shoplifting, anti-social behaviour and thefts of fuel from their petrol stations - much of which is preventable," he said.
"We just ask these stores to work with us to reduce the demands on policing and reduce the risks of disorder and crime."
A Tesco spokesman said: "Over 600 Tesco stores have Black Friday offers available in store.
"In the interest of customer safety a small number of these stores contacted police last night to help control crowds safely and stores are now trading normally."
Black Friday - historically the big sales day in America that follows the Thanksgiving holiday - has been adopted by an increasing number of shops in the UK.
The websites of several retailers, including Tesco, Argos and John Lewis, crashed earlier due to the number of shoppers trying to access them.
Despite its website problems, John Lewis said it was forecasting record online sales by the end of Friday. It said Apple's iPad mini and a discounted food processor were its fastest-selling products in early sales.
Currys said it experienced "astonishing" online demand overnight, with a "pre-planned queuing system" operating.
Many retailers have been advertising Black Friday deals, with Tesco offering discounts of up to 70%.
At about 07:00 GMT on Friday Tesco tweeted that it had "loads" of Black Friday bargains - but that tweet was later deleted.
And on Friday afternoon, Tesco also tweeted that it was having problems with its website, due to "huge demand".
The company has previously said it expects Black Friday to beat Boxing Day sales in 2014.
Its 24-hour stores began selling a minute after midnight, and extra staff have been laid on in some areas.