Despite a smaller increase, rates of reported difficulties with eating were higher in older age groups, which experts described as "particularly concerning".
The proportion of those aged 17 to 19 with a possible eating problem rose from 45% in 2017 to 58% in 2021.
The findings come following three studies done in 2017, 2020 and 2021 involving 2,541 children and young people in England.
Tamsin Ford, professor of child and adolescent psychiatry at the University of Cambridge, stressed the number of children reporting difficulties with eating was not the same as those diagnosed with eating disorders, and said it was not yet possible to know the reason for the sharp increases.
"It's certainly concerning, I think the exact level in the older teenagers is particularly concerning but perhaps not that surprising when this is not eating disorders, it's difficulties around eating," she said.
"Of course, worries about your body and body image in teenagers is known as a high-risk period, so I think the absolute level is surprising, but nobody has ever measured this before.
"It's an increase, it should be concerning and it needs more explanation and more study.
"When we have got a more complete assessment and with all the background data we have on all these children and young people including their social media use...that is something we could explore, but we can only speculate now."
The study also showed more than half of 11 to 16-year-olds reported to spend more time on social media than they meant to.
Some 17% also admitted the amount of interactions, such as likes, comments and shares their posts receive, impacted on their mood.
Other issues highlighted were problems with sleep, with over half (57%) of those aged 17 to 23 reporting to be affected by problems with sleep on three or more nights of the previous seven.
More than a quarter (29%) of six to 10-year-olds also said they had problems with sleep, as did over a third (38%) of 11 to 16-year-olds.
One in six children in England now has a probable mental health disorder, though this figure had not changed significantly since the start of the pandemic in 2020, the study showed.
However, Prof Ford said she was "very wary" of dismissing the stable levels of probable mental health disorders as a "bit of a blip".
"We have done a bit of analysis around what's happening to sub groups but I think we need to be concerned - the signs are that children's mental health was deteriorating from this series of surveys over 20 years, before the pandemic hit," she said.
"We have now got evidence at a population level that it wasn't a blip...some of the (online) surveys do suggest that, certainly in adults, mental health had a bit of a wobble in the first lockdown and then pretty much returned to normal.
"But, of course, the people that fill those in tend to be highly-educated people with access to online materials, and those living in deprivation and ethnic minority groups are under-represented.
"These are not transient issues... I think we should be very wary of dismissing this as a bit of a blip."
Responding to the study, Barnardo's interim co-chief executive Lynn Perry said: "This new data confirms that a worrying proportion of children are struggling with mental health, and this problem is not going away.
"Today's findings show that children who already struggled with their mental health before Covid have faced particular challenges in recent months, and those in poverty and lacking strong family support are also more at risk.
"For all these reasons we are calling on the Government to ensure that mental health support teams are rolled out across all schools in England as a matter of urgency.
"From our direct work with children across the country, we know that they want a mental health system that prioritises early intervention and makes sure they don't 'fall through the cracks', whilst also providing genuine choice in the services they receive - whether that's help at school, online or in the community.
"We need a holistic system that works around each child's needs to promote their wellbeing, with different services working together at a national and local level."
Kadra Abdinasir, strategic lead for the Children and Young People's Mental Health Coalition, said: "Whilst this year's survey does not report a rise in the rates of mental health difficulties from last year, we cannot ignore the fact that rates still remain high and have been deteriorating in recent years.
"We know that accessing support for mental health for children, young people, and their families can be particularly challenging.
"Despite the policy initiatives from Government to improve the availability of mental health support for children and young people over recent years, the survey findings highlight the high numbers of those still not seeking support.
"This suggests that young people still do not know where to turn when they need help.
"Mental health support needs to be truly accessible for all, so that children and young people feel confident that they can get the right support, at the right time."
An NHS spokesperson said: "The pandemic has inevitably had an impact on the nation's mental health, with parents and young people especially stepping up to overcome the challenges posed by the pandemic, and NHS teams supporting over 600,000 children and young people and providing specialist mental health care.
"The NHS is rapidly accelerating plans to treat an additional 345,000 young people as parts of its Long Term Plan, with nearly 200 NHS mental health teams in schools in place covering over one million pupils as well as rolling out a free mental health crisis line for anyone who might need them."