The PSP is billed as a multimedia entertainment device
More than 185,000 were sold in its first four days in UK shops, say official Chart-Track figures.
Rival handheld, the Nintendo DS, sold 87,000 in its launch week in March. The PSP sales account for about £33m.
Sony wants the PSP to appeal to more than just gamers. It also plays films, music, and browses the web wirelessly.
The gadget went on sale in Europe on 1 September, nine months after hit Japanese stores and six months after the US.
Sony expects a million PSPs to be sold in the UK before Christmas.
Shops across the country opened their doors at midnight last week to deal with the demand from gamers, with many reporting that they had sold out. Chart-Track also reported that nine of the 24 PSP games which were available at launch entered the Top 10 official UK games chart this week.
Topping the chart was Ridge Racer, with one in five people buying the game along with the PSP device.
Thumb competition
In the important run-up period to Christmas, the PSP is up against the giant of the handheld gaming arena, Nintendo, which dominates the portable gaming market.
But the PSP is widely touted as a device to appeal to a wider range of people, because it can do more than play games.
Thirty films were available for the device at its European launch, and more titles are on the way. Sony has developed its own discs for films, called UMD.
But Sony has warned PSP owners about a known issue which came to light in the days following the PSP's March launch in the US.
Many gamers returned their devices after the LCD screens appeared to be missing pixels. Sony said in accompanying literature to the device that the "stuck pixel" problem is characteristic of LCD technology.
The PSP went on sale in the UK for £179 (249 euros). In the US, it sells for $249 (£138) plus tax.
Five million PSPs have been shipped by Sony since its launch in Japan late 2004 and in the US in March this year. Sony says it expects to ship 13m by March 2006.
Sony PlayStation Portable

The Sony PlayStation Portable went on sale in the UK on Thursday, September 1. In the three days following the release, more than 185,000 PlayStation Portables were sold. This sets a new sales record on game consoles. The record was previously held by Nintendo, who sold 87,000 Nintendo DS handhelds the first three days after its release. The PlayStation Portable is being sold for £179 in the UK.

Twenty of the 24 games launched with PlayStation Portable are in the top 40. PlayStation Portable games also occupy nine of the top 10 slots on the sales charts. The game Ridge Racer was the most popular, with one in every five people buying both the PlayStation Portable and Ridge Racer  at the same time.

Sony's main competitors in the handheld gaming console market are  Nintendo with the Nintendo DS and Nokia with the nGage. Like Nintendo and Nokia, Sony is marketing the device as being able to do more then just play games. The PlayStation Portable can play specially created versions of poular movies and surf the Internet wirelessly. Sony expects to sell a million PlayStation Portables in the UK before Christmas.