The models affected are the IQ, Aygo, Yaris, Auris, Corolla, Avensis and Verso.
The parts needed to repair the cars will not arrive in the UK until next week, with the first repairs scheduled for 10 February.
Toyota says the process - which should only be carried out by its dealers - takes around half an hour.
A spokesman for Toyota told the BBC no new cars are affected, and dealerships are still taking orders on all models.
The company has also confirmed that there have been dozens of complaints in the US and Japan over brake problems in the Prius hybrid car, but none has been reported in the UK.
The Prius had been unaffected by the sticking accelerator pedal problem.
Toyota is recalling up to 1.8 million cars across Europe over the problem with accelerator pedals. These are on top of the millions of vehicles it is recalling in the US and Japan.
The company said it was not aware of any accidents resulting from the issue and that only 26 incidents involving accelerator pedals had been reported in Europe.
Toyota's UK spokesman Scott Brownlee denied that the firm had delayed the accelerator pedal recall in the UK.
He told the BBC that although concerns were raised about vehicles in late 2008, they were a quality rather than a safety issue.
Toyota said that anyone in the UK who had suffered a problem with their accelerator pedal should call the company's hotline, and should not get the problem fixed independently.
The carmaker is also working with the UK's Driver and Vehicle Licensing Agency, and will write to car owners whose vehicles could be affected - a process that could take 10 days. This will also include owners who have bought the cars second-hand.
The DVLA said that it would have returned the information required to Toyota in two days, by the end of 5 February.
Toyota said it was considering longer working hours and weekend working to get letters delivered to owners. This letter will inform the owner that their car is involved in the recall.
It will be followed by a second letter telling drivers when they can take their vehicle to be fixed. This will be staggered, and the oldest cars will be given priority.
A website that would allow owners to check their vehicles registration number was also being developed.
US authorities said they were looking at the possibility of fining Toyota.
American Transportation Secretary Ray LaHood said safety officials would "continue to hold Toyota's feet to the fire".
He repeated that his agency was studying the possibility of civil penalties against Toyota for safety violations, which could mean fines of millions of dollars for the company.
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