The research looked at the health of more than 18,000 British babies at nine months, three and five years of age.
They charted the children’s height, weight and BMI, and questioned parents on whether they had ever had to attend hospital or take prescribed medications for illnesses.
The researchers from the universities of Leicester, Liverpool, Oxford, Warwick and the National Perinatal Epidemiology Unit, found the earlier a child was born, the more likely it was to suffer a range of health problems.
Being born between one and seven weeks early was identified as the greatest indicator of illness at the ages of both three and five.
Children born between three and six weeks early were found to have an increased risk of asthma and wheezing compared to full-term babies.
But even babies born just one or two weeks early were found to be at higher risk of re-admission to hospital in the first few months of life, compared to those born later on.
Meanwhile, the study found that mothers of children born one or more weeks early were more likely to be single, and less likely to have educational qualifications or work in managerial positions.
Mothers of babies born more than seven weeks early were more likely to smoke and less likely to breast feed for four or more months than those delivered two weeks early or later.
The authors said: "[There is a] continuum of increasing risk of adverse outcome with increasing prematurity, even approaching full term gestation".
The academics are now calling for further research into factors that influence health outcomes for babies born between one and seven weeks early, to inform the provision of obstetric services and planning of health services for children in the early years.
Previous studies have shown poor health outcomes for very premature babies. But few studies have focused on outcomes for "moderately preterm" babies born at 32-33 weeks, "late preterm" babies born and 34-36 weeks and "early term" babies born at 37-38 weeks. Babies born at 39 weeks onwards are considered "full term".
The researchers said: "These groups of babies represent a relatively large proportion of births, and therefore, even modest increases in health problems may have important implications for public health and for the allocation of health and educational resources."
