Retailers have reported frenetic scenes as Boxing Day bargain hunters rushed to beat reduced trading hours in many stores.
Because 26 December falls on a Sunday this year, trading hours are restricted for many - in England, larger stores can trade for only six hours.
Some shoppers were hoping to beat a VAT rise from 17.5% to 20% on 4 January.
Shopping centres across the UK reported "phenomenal" trading, with queues outside some stores.
Sue West, operations director of London's Selfridges, said this year's sale was "more challenging than we've ever had to do because of the late opening".
The BBC's Ben Geoghegan said shoppers there - some of whom had been queuing for up to 12 hours - were "screaming with relief" when doors opened at the store at 1100 GMT.
'Don't move, improve'
Many retailers are offering heavy discounts to make up for the impact on sales of freezing pre-Christmas temperatures and heavy snow.
Trevor Pereira, commercial director at Capital Shopping Centres PLC, which has interests in 13 regional shopping centres including including Braehead in Glasgow, Lakeside in Thurrock and Metrocentre in Gateshead, said retailers saw demand for the "higher priced items which spans practical white goods right through to the more desirable, fashion-led purchases of IT-bags and designer watches".
"Homewares have also proved popular, which may well signal the trend for another year of 'don't move, improve'," he said.
Peter Cook, director of the White Rose Centre in Leeds, said he was expecting 65,000 people through his doors on Sunday.
"In terms of previous years, it's started much better," he said.
"People are spending a lot of money."
By 45 minutes after the centre opened, "every single space" had been taken, he said.
At the Meadowhall Centre in Sheffield, the inner ring road car park had reached its 9,500 space capacity before the shops opened for business at 1100 GMT.
The Arndale Centre in Manchester had "phenomenal" trading, and was expecting 170,000 shoppers through its doors by close of trading.
"It is difficult to get into some of the shops because of the sheer volume of people," said general manager Glen Barkworth.
"By 0930 we had 20,000 people in the malls and the shops only opened at 1100.
"We went around the shops to ask them to open early to extend the browsing time to allow customers into the stores."
Shoppers began queuing as early as 0500 GMT at Braehead shopping centre, according to general manager Peter Beagley.
"I've no doubt that shoppers also had their eye on the VAT increase in January and were buying items to save on paying the extra VAT," he said.
Although Braehead officially opened at 1000 - shops in Scotland are subject to different legislation - some of the stores including Next and River Island had "got off to an excellent start" at 0700, he said.
By 1300 GMT there were 70,000 shoppers at the Trafford Centre on the outskirts of Manchester.
Sunday trading hours
Gordon McKinnon, director of operations at the centre, said the sales had "gone off like a rocket".
But he said the government needed to "take a long hard look" at the law on Sunday trading hours, given the tough trading environment shops had endured over the past 12 months.
Some stores - such branches of Next outside Scotland - are holding off opening their doors to their sales until Monday.
Shoppers in London's Westfield centre - who also had to contend with a Tube strike - said they were frustrated by the delay in getting into stores because of Sunday trading rules.
"We're meant to be in a time of economic hardship, but here we've got all these people with money to spend wandering around not spending it," said James Dixon, 36, of Hayes, west London.
"If it's the law, then the law should change."
Emma Wills, 27, of Putney, south-west London, added: "It's annoying because there's even less chance of beating the rush."
A man has been arrested after a teenager was shot in the leg in Birmingham's Bullring shopping centre.
Armed police officers were called to reports of an incident involving a gun at about 1420 GMT and a 19-year-old man was found with the gunshot injury.
Earlier, the Bullring's managers had said they expected more than 180,000 people to pass through its doors.
Police said a number of areas had been cordoned off both inside and outside the shopping centre while the investigation continued.
New West End Company, which represents 600 retailers in London's West End, said some stores would be open for up to 16 hours on Monday to compensate for the restrictive Sunday trading hours.
Many consumers were also expected to avoid the High Street and shop online the comfort of their own homes.
Comparison website moneysupermarket.com forecasts this year's Boxing Day sales to be the biggest ever, estimating that the UK will spend £323m over the internet on 26 December.