The research found one in three parents (33 per cent) admit to being anxious about their child finding friends when they start school.
Just in excess of one in 10 (11 per cent) said their main worry was that their son or daughter would not be able to keep up with the school work.
The same proportion were concerned that their youngster would not ask for help when they needed it.
Action for Children, which commissioned the poll, said a child's first day at school could be an anxious time, sometimes more so for parents than the pupils themselves.
Jan Leightley, the charity's executive director of operations, said its centres helped prepare youngsters by giving them "a place to play with other children, to learn to make friends and to develop their language skills".
Previous surveying by Action for Children of its own centre managers found two-fifths felt children were needing more help to reach basic milestones such as being toilet trained and being able to follow simple instructions.
The YouGov poll questioned 9,015 adults including 2,267 parents of children aged 18 or under in February.