The bus crashed yesterday into several cars and a lamppost before hitting the supermarket on what would have been a busy shopping day in the city centre.
"Boy (8) and woman confirmed dead after Coventry bus crash," West Midlands police said in a tweet.
The boy was on the upper deck of the bus.
"It was absolute chaos," Maneer Fiaz, an eyewitness who took part in rescue efforts as bystanders rushed to help, told Sky News.
A nine-year-old girl also on that deck was seriously injured and is one of five people being treated in hospital after the incident.
