Toyota says that 4,556 of its GT86 sports cars are affected by the fault in the UK, though the manufacturer has stressed that the issue has not yet caused any injuries.
Drivers of the cars that need repairing will be contacted by the firm directly to be booked in for a service that has been estimated to take around an hour.
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A similar recall has been issued in Australia, where some 15,000 vehicles built between April 2012 and March 2015 are said to need repairing.
The fault, which also affects the similar Subaru BRZ, concerns the airbag cover found over the driver’s knee.
It has been found that this flap can interfere with the car’s EPAS electric power steering system, causing essential wiring to disconnect.
And it is this which can create lapses in the power assistance, making steering feel heavier and causing a yellow dashboard warning light to turn on.
Toyota has said that once it has carried out the repair, which involves replacing the EPAS control unit and wiring harness, the vehicle should become much more responsive.
Earlier this year, the manufacturer unveiled a larger concept version of its acclaimed GT86, with more headspace and extra room in the boot.
The concept was aimed at mixing the sporty feel of the original model with the added versatility of an estate car, making it a good match on the track and for everyday driving.
In 2012, Toyota was forced to issue a recall for its Land Cruiser Amazon models, which were also affected by a steering problem.
Nearly 350 vehicles in the UK were called in for repairs following two incidents in Europe, though these did not result in accidents.
It followed an international recall of some 270,000 cars in the Lexus and Crown range that were affected by engine problems.
While no accidents were reported as a result of these faults, the manufacturer moved to replace valve springs and other key parts as a precautionary measure.