One of the main motivations given for the proposed new expansion of grammar schools in England is to improve social mobility. We assess the role of existing grammar schools in promoting social mobility by examining access to grammar schools, differentiating among the 85% non-poor pupils using the National Pupil Database. We find stark differences in grammar school attendance within selective areas by socio-economic status, even when comparing pupils with the same Key Stage 2 attainment. High attaining children from the most deprived backgrounds are significantly less likely to attend a grammar school compared to similarly high attaining children from the least deprived backgrounds. Given these large inequalities in attendance to grammar schools, conditional on achievement, it is hard to see how such a system would promote the aim of improving social mobility.