The manufacturer will contact owners of the affected models - BMW 1 Series, 3 Series, Z4 and X1 petrol and diesel models made between March 2007 and August 2011 - in the next three weeks, a spokesman said.
The Driver and Vehicle Standards Agency (DVSA) said last week BMW had failed to alert UK authorities to 19 cases of electrical faults in one of its models.
Former Gurkha soldier Narayan Gurung, 66, died on Christmas Day 2016 when he crashed his Ford Fiesta into a tree in Hampshire while swerving to avoid a BMW car which had cut out due to an electrical fault, an inquest in Woking, Surrey, was reportedly told.
But an investigation by BBC Watchdog Live found the issue could be in a wider number of vehicles than those covered by the original recall of 36,410 cars in 2017.
A BMW spokesman said: "Now we recognise the need to widen the recall to capture a larger cohort of cars. We are widening the net as a precaution."
He added the fault could be fixed within two hours and involved replacing a plug.
The firm has not advised customers to stop driving the vehicles.
Mwape Kambafwile told the BBC he stopped driving his BMW 3 Series car after it cut out completely while he was driving in December 2016.
He said: "I just thought to myself if I was driving on the motorway with my family in the car, that could have been very dangerous.
"I took it to BMW. The next day they called me to say they had found a fault, it looks like the cable had burnt out and no current was passing through the fuse box.
"I felt so uncomfortable driving it that we took taxis, I walked to work every day. It was a nightmare, it wasn't safe enough to drive."
Watchdog Live will air on Wednesday at 8pm on BBC One.