Steve Settle, Toyota GB Customer Services Director, said: "Toyota service centres will be working extended hours and weekends... we have implemented the recall as quickly as possible."
Toyota will prioritise those customers whose cars have been identified as having the fault via the Toyota customer helpline.
Mr Settle urged drivers to contact their local dealer or ring the company's hotline in order for their vehicle to be booked-in for the procedure, which involves a piece of metal being fixed into the accelerator pedal.
The company has said that older models will also be given priority as the fault occurs when the pedal becomes worn.
Prius drivers affected by that recall should also receive letters, but if they are concerned they should contact their dealer or ring the company's hotline.
Meanwhile, in the US, a Congressional committee has cast doubts on Toyota's plans to fix its two acceleration problems.
In a memo to lawmakers it said there was growing evidence that neither Toyota nor federal safety officials had identified all the faults.
The memo cited "substantial evidence" of redesigned floor mats failing to stop the pedals sticking under the mats.
Toyota's president has apologised for the problems caused by the raft of faults. But he has come under criticism in Japan itself from the country's transport minister for not reacting quickly enough to recall faulty vehicles.
There have been complaints in Japan and the US that the brakes on the Prius momentarily fail when driven on rough or slippery road surfaces.
There have been no reports of any such accidents in the UK.
Before it announced the Prius recall in Japan, Toyota estimated its losses would reach $2bn (£1.23bn) in costs and lost sales.
The Prius recall is expected to send this figure even higher.
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