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 British climber trapped on Mount Everest after the earthquake in Nepal has said rescuers face "a race against time" to reach his group
People who suffer from back pain may have closer links to their chimpanzee ancestors, according to researchers.
David Cameron will say the Tories are the party of the "grafters, roofers, retailers and plumbers" as he set out plans to help small firms