The photo of Jack laying on the hospital floor with an oxygen mask was first published by the Yorkshire Evening Post on Sunday and has since been picked up by a number of national newspapers.
But when the Prime Minister was this morning being interviewed by ITV News Political Correspondent Joe Pike in Grimsby, and was asked to look at a photo of Jack, Mr Johnson did not look down at the photo on Mr Pike's phone, instead saying he would "study it later" as he attempted to steer the conversation on to Tory investment in the NHS.
Jack’s mother Sarah Williment covered him with coats to keep warm as he waited for a bed at Leeds General Infirmary.
She had taken him there last Tuesday fearing he had pneumonia.
In a clip of the interview posted on Twitter, Mr Pike said to Mr Johnson: "You refuse to look at the photo. You've taken my phone and put it in your pocket Prime Minister."
Mr Johnson then took the phone out of his pocket, looked at the photo on the screen, and said: "It's a terrible, terrible photo. And I apologise obviously to the families and all those who have terrible experiences in the NHS.
"But what we are doing is supporting the NHS, and on the whole I think patients in the NHS have a much, much better experience than this poor kid has had.
"That's why we're making huge investments into the NHS, and we can only do it if we get Parliament going, if we unblock the current deadlock, and we move forward."
But Mr Johnson did not escape scrutiny as during a press conference in his next campaign trail stop on Teesside he was asked by BBC Political Editor Laura Kuenssberg why he did not initially look at the photo.
However the PM again spoke on policy and answered: “I am very proud of what we are doing to rebuild Leeds General Infirmary. It will be a fantastic project. I hope everyone will vote for One Nation Conservatism.”
Mr Johnson was then questioned a second time, this time by ITV’s Paul Brand. Mr Brand said one of Mr Johnson’s “biggest challenges in this election is to persuade people [he] really [does] care”. He asked what taking Mr Pike’s phone away said about that.
But Mr Johnson said he had already answered the question and added: “We are not only investing in children’s services in Leeds. But we’re also rebuilding the whole Leeds Infirmary from top to bottom.”
Shadow health secretary Jonathan Ashworth said: "Refusing to even look at an image of a child suffering because of Conservative cuts to the NHS is a new low for Boris Johnson. It's clear he could not care less.
"Don't give this disgrace of a man five more years of driving our NHS into the ground. Sick toddlers like Jack deserve so much better."
Labour leader Jeremy Corbyn held up a copy of the Daily Mirror, which had followed up the Yorkshire Evening Post's coverage this morning, as he spoke at a rally in Bristol.
He said: "They've had nine years to sort this out."
Earlier, Mr Johnson apologised to "everybody who has a bad experience" in the NHS after the story of four-year-old Jack emerged.
Ms Williment said her son was eventually moved to a ward, where he waited for five hours on a trolley before a bed was found at 3am.
Diagnosed with flu and tonsillitis, Jack was allowed to be taken home at lunchtime.
She said: "I am frustrated about the system and the lack of beds, which I am presuming is due to a lack of funding to the NHS to deliver the services that are required."
Asked about the incident during an interview on LBC, the Prime Minister said: "Of course I sympathise very much and I apologise to everybody who has a bad experience.
"By and large I think the NHS do an amazing job and I think that they deserve all praise for the service they provide - but they do need investment and that's why we're doing it now.
"But they need investment from a one nation government that really cares and understands - that's us that cares and understands - and you need long-term funding."
Dr Yvette Oade, Chief Medical Officer at Leeds Teaching Hospitals NHS Trust, said: "We are extremely sorry that there were only chairs available in the treatment room, and no bed. This falls below our usual high standards, and for this we would like to sincerely apologise to Jack and his family."