University of Portsmouth researchers found just under 16 percent of 11-year-olds and almost 19 percent of 15-year-olds steered clear of particular foods.
Around 12 percent in both groups claimed an adverse reaction to one or more foods.
But the Journal of Allergy and Clinical Immunology study found 2.3 percent in each group had an allergy or intolerance.
Peanuts, dairy products, wheat and fish were common allergies, both in the group reporting problems and those who did have allergies or intolerances.
Specialists use the term food hypersensitivity syndrome, or FHS, when discussing both intolerances and allergies.
Our concern is that if the world and his wife say they have an allergy, those who really do will find it increasingly hard to be taken seriously
Muriel Simmons, Allergy UK
The study was carried out by Dr Taraneh Dean, in conjunction with the David Hide Asthma and Allergy Research Centre on the Isle of Wight.
The researchers surveyed 757 11-year-olds and 775 15-year-olds.
The children and their parents completed a questionnaire on adverse reactions to food – and symptoms they displayed, and which foods they avoided.
Children were then given skin tests and food challenge tests – where they were asked to eat the food or foods they felt could cause problems.
Dr Dean said: “We were surprised that such a high proportion of people in this age group perceived they had a problem, and at the number who avoided certain food groups.
“Some said they didn’t have a problem with certain foods, but avoided them anyway.”
Dr Dean added: “What this study suggests is that there is a public perception of an increase in FHS, which is not borne out by objective clinical assessment.
“The scale of the problem should be small, but self diagnosis is making the issue larger than it should be.”
She said doctors may need to spend more time investigating patient reports of FHS so they can put both the child’s and the parent’s minds at rest.
Muriel Simmons, chief executive of Allergy UK said: “A lot of people – whether young or not – talk about allergies or intolerances.
“But only 2 percent have got a food allergy.
“We know young people are increasingly concerned about allergies.
“Whilst we want them to be aware, we don’t want them to restrict their diets.”
She added: “Allergy is a big problem for some people. Our concern is that if the world and his wife say they have an allergy, those who really do will find it increasingly hard to be taken seriously.”