Scientists believe the rise could be due to more women eating peanuts when they are pregnant or breastfeeding.
However, it is also possible that children become sensitised by coming into contact with pre-packed food contaminated with traces of peanuts.
A team from the David Hide Asthma and Allergy Research Centre on the Isle of Wight found that the proportion of children who tested positive for peanut allergy has tripled since 1989.
The researchers tested 1,246 children born between 1994 and 1996 for allergy to peanuts.
Each child got a skin prick test for peanut allergy, and their parents were asked about a history of asthma, hay fever, eczema and specific food allergies.
The results showed that 41 (3.3%) of the children had a positive response to peanuts. A similar study in 1989 found a positive response rate of just 1.1%.
Other allergies
Half of the children who tested positive to peanut allergy had a history of asthma, and nearly all had eczema.
Peanut allergy is not common in the population but it can be deadly.
Allergic reactions can range from hives, swelling and vomiting to breathing problems and a swelling of the tongue or throat which can be suffocating.
Peanuts can be hidden in many food stuffs and sufferers are advised to carry epinephrine shots with them at all times in case they accidentally swallow them.
Doctors say women who have a family history of allergy should not eat peanuts while pregnant or breast feeding, and infants with such a family history should not be given peanuts to eat.
A study by the Food Standards Agency found that 56% of pre-packed food items had the potential to trigger peanut allergy.
David Reading, director of the Anaphylaxis Campaign, told BBC News Online the research bore out the charity's anecdotal experience that peanut allergy appeared to be becoming increasingly common.
"Although it is only rarely fatal, it does present a tremendously important problem for public health," he said.
"Peanut allergy can cast a real shadow over family life because of the management strategies needed to handle it.
"To know that your child is potentially at risk can be a tremendous emotional burden."
The research is published in the journal Journal of Allergy and Clinical Immunology.