The ITV News presenter said the show stopped being "a laugh and a joke" for her when the former health secretary arrived and she felt she was "walking a tightrope" in her interactions with him.
White told the Daily Mail she was acutely aware she had a duty to her profession and to the families awaiting the public inquiry into the actions of Hancock and the government during the COVID-19 pandemic.
"I was doing the mental arithmetic in my head, and it had stopped at that point for me just being there and having a laugh and a joke – that finished when Matt came," she said.
Watch: Ant and Dec joke about Matt Hancock's jungle entrance video
White added: "I have interviewed enough of the families that have lost loved ones during the pandemic. I am one of those."
The star, who is also a regular on Loose Women, became the first celebrity to be eliminated from the show on Friday night.
She had earlier become the first celebrity to request to be removed in the middle of a bushtucker trial, shouting the show's name while taking part in the harrowing "Watery Grave" challenge.
White was one of the campmates most responsible for grilling Hancock about his affair and handling of the pandemic when he entered the reality TV series this week.
She also turned down an opportunity to sleep in the relative comfort of the camp's RV alongside Hancock, despite being crowned deputy camp leader.
"I didn't want anyone to feel like I was being too sympathetic to Matt because that would jeopardise the job that I love and jeopardise my journalistic integrity," said White.
The journalist said cosying up with Hancock on television would have "shattered the impartiality" that has been a cornerstone of her broadcasting career.
White added: "In my heart I felt if I didn't represent those people who are still grieving and still hurting, if I don't think about them and ask the questions that I want to know regarding his reasoning for going in the jungle… then I'm not doing my job.
"It went from me having a laugh to me constantly worrying about whether or not I could still do my job when I came out."
White reflected positively on her time as part of the show and said she's already missing fellow campmates Sue Cleaver and Boy George, with whom she bonded.
She also revealed she has been working hard to wash the jungle off her, showering three times and washing her hair twice in the first 24 hours alone.
I'm a Celebrity... Get Me Out of Here airs nightly at 9pm on ITV.
Watch: Famous faces give their views on Matt Hancock's I'm a Celeb stint