Omar Salem told Mr Johnson his newborn daughter had to wait two hours for treatment in the children’s ward at Whipps Cross University Hospital, in east London, after she nearly died on Tuesday.
"My daughter nearly died yesterday,” he said.
"A&E guys were great, but we then came down to this ward here. It took us two hours... for [unclear] to be put into my seven-day-old daughter."
Mr Salem, who is a Labour activist, claimed the NHS was being destroyed and that there were not enough doctors and nurses during a two-minute conversation on Wednesday.
He said the situation was “not acceptable” and told the Prime Minister: “There are not enough people on this ward, there are not enough doctors, there’s not enough nurses, it’s not well organised enough.
“The NHS has been destroyed… and now you come here for a press opportunity.”
Mr Johnson replied that there were “no press here” but the father quickly pointed to the cameras at the children’s ward.
Mr Salem said: “What do you mean there’s no press here, who are these people?”
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The Prime Minister then tried to move on and told the father he was there to find out about the situation but the dad was having none of it.
“It’s a bit late, isn’t it?” Mr Salem said. “Years and years and years of the NHS being destroyed.”
Following the confrontation, Mr Salem responded to suggestions that his actions had been politically motivated because he is a Labour activist.
The Prime Minister’s spokesman said Mr Salem was understandably “very distressed” and that the PM was “not going to hide away from those circumstances when he goes on these visits.”
Members of the public have confronted the Prime Minister on numerous occasions in recent weeks.
Mr Johnson was told to “get to Brussels” while being interviewed by the BBC in Leeds on September 6.
A man was angry Brexit had not been sorted.
A woman then challenged the PM over austerity when he visited Darlington last week.
She told him: “People have died because of austerity. And you’ve got the cheek to come here.”
Later that day he was heckled by charity worker Ben Gilchrist, 41, who checked him over his decision to prorogue parliament.