In Glasgow, shoppers queued for two hours waiting for Braehead Shopping Centre to open its doors.
A spokeswoman for Selfridges said about 2,000 people waited outside the London store to grab the first bargains.
She said: "It was mental when they came into the store. I've never seen anything like it.
"People were running into the store and grabbing bags. Some women had four or five bags in their hands. Security had to get more people down to the store to help."
She added that it took some shoppers as much as an hour to queue for the tills.
Jace Tyrrell, of the New West End Company, which represents more than 600 traders in London's Bond Street, Oxford Street and Regent Street, said: "Are they mad? Well, it's very tempting when you've got designer handbags with 60% off."
And at the Trafford Centre in Manchester, staff said there were more shoppers than on the same day last year.
Some High Street stores, including John Lewis and Marks & Spencer, began sales on their websites on Christmas Day.
John Lewis recorded its busiest ever online sales between 7pm and 8pm and said its Christmas Day traffic on its website was 12 times higher than last year.
London's Brent Cross Shopping Centre saw 30,000 people through its doors by midday
The centre's Norman Black, said more than 100 of its stores had started their sales.
Others, such as M&S, John Lewis and Fenwick would begin their sales on 27 December with "significant reductions", he added.
We'll see the full December figures in a few weeks, but they won't be pretty
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