London Fire Brigade said the concrete fascia of the building collapsed on to the car, which was in Kingsway. Around 20 firefighters helped with the rescue, freeing the trapped pair from the car.
A spokesman said: "Another woman travelling in the car managed to get out of the vehicle before the brigade arrived.
"Around 10 people were evacuated from nearby buildings as a precaution."
More top news
A woman who was "dragged away" by a crocodile as her friend tried in vain to rescue her is reportedly still missing in Australia.
Police say at least one gunman armed with a high-powered rifle, began "shooting randomly" resulting in the death of a man in his 50s.
Ever wondered what the most expensive seaside town in Britain is? Find out here.