The research, led by Peter Taylor of Cardiff University, found that babies born with the gene plus low thyroid hormone levels are four times more likely to have an Intelligence quotient (IQ) below 85.
An IQ under 85 is considered below average while an IQ measuring anywhere between 85 to 114 is considered average.
In the study, Taylor and colleagues, including those from Bristol University, measured the IQs of 3,123 children aged seven and analysed their DNA.
They were looking for a gene that produces an enzyme called deiodonase-2, which helps to make thyroid hormone available within cells.
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In children with normal thyroid levels the faulty enzyme has little effect, but in those where the levels are already low the thyroid hormone falls to such low levels that the brain cannot develop properly, researchers found.
They estimate that 4 per cent of all babies in the UK are born each year with the gene plus low thyroid hormone levels.
The discovery raises the prospect of a new test for newborns to spot those with the low-IQ gene variant as well as low hormone levels.