The strengths and difficulties questionnaire (SDQ) consist of five sub-scales that have been used to measure internalising and externalising symptoms in children, typically by combining sum scores of two sub-scales each, and pro-social behaviours. However, the different possible factorial structures that represent these symptoms have not been formally tested in a nationally representative sample of UK children. In addition, it is necessary to assess whether the SDQ is interpreted similarly across subgroups of the population. Exploratory and confirmatory factor analysis were used to test three competing structures for the parent-reported SDQ collected at age 11, the start of adolescence, in the UK Millennium Cohort Study (n = 11,519), and measurement invariance was assessed according to sex and a measure of deprivation of the area in which households lived. Internal consistency using ordinal alpha, internal convergent validity and external discriminant validity using average variance explained (AVE), and predictive validity were assessed. A five-factor model and a model with two second-order factors for internalising and externalising symptoms had better model fit than a three-factor model. For both structures, invariance was demonstrated across sex and area-level deprivation. AVE scores for the five-factor model indicated that peer and emotional problems factors were measuring a similar construct, as were the hyperactivity and conduct factors. In the second-order model, AVE scores indicated internalising and externalising symptoms were distinct constructs. A second-order model with two factors for internalising and externalising symptoms is appropriate for use in a cohort of UK children born in 2001/02, and our finding of invariance across sex and area-level deprivation indicate that the SDQ can be used in analysis investigating differences in symptoms across subgroups of the population.