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Tux Machines (TM)-specific
Its European launch was delayed to ensure supplies for its US debut.
Many shops said they had already sold out of their pre-order allocations, as fans queued through the night for them.
Sony said the demand had been huge. "We think it will be the biggest UK launch in the history of our business across all manufacturers," a spokesman said.
Sony expects a million of the gadgets to be sold before Christmas.
The gadget went on sale in Europe nine months after hit Japanese stores and six months after the US.
Tesco said it expected to sell out by the end of the weekend.
Five million PSPs have been shipped by Sony since its launch in Japan. Sony says it expects to ship 13m by March 2006.