The prime minister was visiting the maternity ward at Whipps Cross Hospital when he was approached by a father.
The man, who is also a Labour activist, told Boris Johnson that the ward was understaffed and the NHS was being destroyed.
A spokesman for the prime minister later said Mr Johnson was visiting public services to see for himself the reality of the situation.
They added the prime minister was “not going to hide away from those circumstances when he goes on these visits, and so obviously is keen to talk to people and empathise and see what he can do to help.
“It’s also a reminder of why exactly he is so keen to make the NHS a priority.”