24 people with minor injuries have been taken to St Thomas' hospital, a London Ambulance Service spokesperson has said.
Several others in a more serious condition are being treated at the scene of the crash.
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The Professional Footballers Association says 302 players sought support in the first seven months of 2017.
Scotland Yard said it was investigating eight cases of fraud involving people allegedly claiming payments in the wake of the disaster.
The robbery is being connected to a spate of thefts in south east London.