Almost two thirds (64 per cent) of eight to 16-year-olds polled said they would be "relieved, not bothered or happier" if winning or losing were not a factor.
However, 22 per cent of parents said they would have less interest in watching school sport if it was not competitive.
The poll, by Marylebone Cricket Club and charity Chance to Shine, surveyed 1,000 children and 1,000 parents.
Asked how they would feel if winning and losing was removed from sport, 30.3 per cent responded that "as long as I get to play I'm fine with it", one in five said "it wouldn't bother me" and one in 10 said "it would make me less anxious".
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The figures have caused concern at Chance to Shine, which seeks to increase cricket participation in state schools.
"We want to teach children the importance of playing sport competitively and fairly and for them to see the benefits that it can bring to their lives."
The survey also found that 89.3 per cent of parents of eight to 16-year-olds believed it was "important" or "very important" for their children to experience victory or defeat in sport.
Just under two in five (39 per cent) children said their parents would be less interested without a competitive factor.
About 86 per cent of the children surveyed, along with 97 per cent of the parents, said that they felt some mothers and fathers were more concerned about winning than the children themselves.
Asked what was most important about school sport, both parents and children agreed that teamwork and exercise were the key aspects.
The study follows a report by education watchdog Ofted last year that said there was not enough strenuous physical activity in school physical education lessons.