It also shows moderate drinking, around one a day, does not affect the child’s IQ and other brain functions.
However, high levels of consumption – nine or more drinks a week – were linked to a lower attention span at the age of five.
The findings contradict official guidance, which says alcohol is best avoided in pregnancy and when trying to conceive.
Previous research has suggested the odd tipple does not affect intellectual or behavioural development, but this is the first significant evidence that occasional binge drinking in the early weeks of pregnancy is unlikely to irrevocably harm the baby.
Danish doctors behind the research said the findings should not be taken as a green light for pregnant women to binge drink, defined as having five or more drinks on one occasion.
Joint author Professor Ulrik Kesmodel, of Aarhus University Hospital, said it was clear that heavy, continuous drinking was detrimental to the unborn child.
Heavy drinking in pregnancy is linked to Foetal Alcohol Spectrum Disorder in children, which can cause physical, mental and behavioural problems. Newly pregnant women were often concerned their baby had been conceived at a time when they may have been binge drinking, said Prof Kesmodel.
Their weekly drinking habits were recorded, with low consumption defined as one to four drinks, moderate as five to eight and high levels as nine or more. Women who did not drink during pregnancy were included for comparison. In Denmark, one standard drink is equal to 12 grams of pure alcohol, compared with a unit of 7.9g in the UK.
Five studies published in BJOG: An International Journal of Obstetrics and Gynaecology looked at the effects of alcohol on IQ, attention span, and functions such as planning, organisation and self-control in five-year-old children.
The study by Danish researchers contradicts the official advice warning pregnant women to stop drinking
No differences in IQ and other tests were found between children whose mothers had up to eight drinks a week in pregnancy compared with those abstaining.
There was also no effect on a child’s selective attention and sustained attention in children of mothers drinking up to eight drinks a week. However, nine or more drinks a week were associated with a lower attention span among five-year-olds.
Prof Kesmodel, a consultant gynaecologist who carried out the studies with Erik Lykke Mortensen at the University of Copenhagen, said: ‘We were not so surprised to find no effects from lower levels of drinking, as previous research suggested this, but we didn’t even find subtle effects caused by low to moderate and binge drinking.
‘But the key message is that drinking during pregnancy is not beneficial and additional studies should be undertaken.’
The Department of Health said: ‘Our advice remains that women who are trying to conceive or are pregnant should avoid alcohol.’