Health minister Norman Lamb told the BBC he is "very interested" in banning the use of face-down restraint. He said: "If that is possible, it should be done."
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Police are trying to find the driver of the car following the incident in Kingfisher Close, Brownhills.
An unnamed man died at the scene, while a woman was pronounced dead after being taken to St George's Hospital, Tooting, south-west London.
Eastern areas will see a few showers coming in on the northeasterly breeze