The trend was seen in a large Pakistani community in Yorkshire, where blood relative marriages accounted for nearly a third of abnormalities such as heart and lung disorders and Down's syndrome.
A slightly lower increase in risk applied to older white British mothers who gave birth after the age of 34.
Both findings emerged from the Born in Bradford (BiB) study, which is tracking the health of 13,500 babies born at Bradford Royal Infirmary between 2007 and 2011.
Having closely related parents was found to be a bigger risk factor for birth defects than a mother who smoked or was obese, or was socially deprived.
The overall rate of birth abnormalities among the BiB babies, 306 per 10,000 live births, was almost double the figure for the UK.
Of 5,127 babies of Pakistani origin, 37 per cent had married parents who were first cousins.
This compares with less than 1 per cent of married couples in Britain as a whole.
Consanguinity - marriage between blood relatives - is a deeply entrenched tradition in many parts of the world.
Globally, more than a billion people live in communities where the practice is commonplace.
Study leader Dr Eamonn Sheridan, from the University of Leeds, stressed that in real terms the chances of having a baby with a birth defect remained low.
He said it was important to note that the absolute increase in risk was small, from 3 per cent to 6 per cent.
Professor Neil Small, from the University of Bradford, who co-authored the research published in The Lancet medical journal, said: "This is the first study that has been able to explore all causes of congenital anomaly in a population where there are sufficient numbers in both consanguineous and non-consanguineous groups to come to reliable conclusions.
"Clear and accessible information on these small but significant avoidable risks should be widely disseminated to local communities and be included as part of antenatal counselling and in the planning of healthcare services."
Irrespective of ethnic origin, a high level of maternal education roughly halved the risk of having a baby with a birth defect, the study showed.
Writing in the journal, the researchers concluded: "Our findings confirm that the offspring of consanguineous unions have an increased risk for congenital anomalies, which is independent of deprivation.
"Couples contemplating such unions should be advised of these risks; however, advice should be given with sensitivity and cultural awareness.
"The public health implications are important.
"In regions with large communities that practice customary consanguineous unions, levels of congenital anomaly will be higher than average."