Researchers from Bristol University analysed data from the Avon Longitudinal Study of 13,978 children born in the nineties.
They found that the five per cent of babies born at 32-36 weeks (late-preterm) were least likely to do as well on their Key Stage 1 (KS1) tests compared to babies born at term.
Around 71 per cent of the late-preterm babies were successful in their KS1 tests, compared to 79 per cent of children born at term.
For the individual subjects, 78 per cent of children born between 32 and 26 weeks successfully passed their reading test, compared to 85 per cent of full term children. On the writing test, 77 per cent of late-preterm children passed compared to 84 per cent of those born at term, and 82 per cent of children born early passed their maths test against 89 per cent of term children.
According to the researchers, babies born between 32 and 36 weeks make up 82 per cent of all premature births and six per cent of all live births in the UK.
Previous research has shown that premature babies are more at risk of developmental delay, cerebral palsy and learning difficulties, but little has been known until now about how well late-preterm babies in the UK fare at school compared to babies born at full term.
Dr Philip Peacock, who led the study, said, ‘Given that children born late-preterm make up the majority of all preterm births, and comprise around six per cent of the population, this group warrants more recognition and surveillance than is currently provided.
'We recommend children born late-preterm receive a school readiness and educational assessment prior to starting school to help identify potential learning problems.
'Early intervention within this vulnerable group of children may help reduce the burden of school problems and their associated consequences.
Separate research, also published this week, found that babies born just a few weeks early are more likely to develop behavioural or emotional problems as toddlers.
The study, Early School Attainment in Late-Preterm Infants, is published online in the journal Archives of Disease in Childhood.