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.
- 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"
- 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
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."
What is wrong with us? Why are we becoming more and more like our American counterparts? Not in the good ways, but finding the worst and most savage and destructive behaviours and thinking, “Hey! I’d like to be like that!”