The boffins have defined "light" drinking as up to two drinks a week throughout pregnancy.
The study of 12,500 three-year-olds even found a lower risk of some problems in children of such drinkers.
However, experts were divided over whether the study was reassuring or could lull women into a false sense of security, reports BBC.
Although experts say pregnant women, or those trying to conceive, should avoid drinking alcohol, but if they do choose to drink, they should drink no more than one or two units of alcohol once or twice a week and should not get drunk, the researchers said.
The relationship between sustained heavy drinking in pregnancy and health problems for the child is well-established.
In most severe cases, boozing can cause miscarriage or stillbirth, or permanent damage to the growing fetus.
A small number of babies in the most severe cases can be born with "fetal alcohol syndrome", with symptoms including growth and mental retardation.
To reach the conclusion, the University College London team asked mothers about how much alcohol they had drunk during pregnancy when their babies were nine months old.
Light drinking was classed as ranging from one drink every so often to two drinks per week, while moderate drinking was between three and six units per week or three to five per one occasion.
Heavy drinking was regarded as seven or more units per week or at least six per occasion.
While 63percent of the mothers had abstained from alcohol completely during pregnancy, 29percent had been light drinkers, 6 percent moderate and 2 percent heavy, the study found, which has been published in the International Journal of Epidemiology.
The researchers then went back when the children were three to ask about their behavior and understanding.
The study found boys born to light drinkers were 40 percent less likely to have conduct problems and 30 percent less likely to be hyperactive than those whose mothers had abstained.
They also scored more highly on vocabulary tests and on identifying colors, shapes, letters and numbers.
Dr Yvonne Kelly, the epidemiologist who led the study, said: "Our research has found that light drinking by pregnant mothers does not increase the risk of behavioral problems and cognitive defects. The reasons behind these findings might in part be because light drinkers tend to be more socially advantaged than abstainers, rather than being due to the physical benefits of low level alcohol consumption seen, for example, in heart disease.
"However, it may also be that light-drinking mothers tend to be more relaxed themselves and this contributes to better behavioral and cognitive outcomes in their children."