In 2018 the UK government launched a £50 million scheme to fund the expansion of existing grammar schools provided that they increase efforts to attract more pupils from socioeconomically disadvantaged backgrounds. This initiative assumed that grammar school attendance boosts the educational attainment and the higher education progression rates of pupils judged to be of high ability. It is already well established that grammar school pupils' higher average levels of educational attainment are due largely to their academic and social selectivity. The evidence in relation to higher education enrolment conditional on educational attainment, however, is more mixed. This paper sets out to update and improve on previous studies of the impact of grammar school attendance on higher education enrolment. Our analysis of data from the Next Steps longitudinal survey linked to National Pupil Database records finds that propensities to enrol in higher education generally, and at prestigious Russell Group universities specifically, are no better for grammar school pupils than for non-selective state school pupils with the same level of attainment at GCSE and A-level. This nil effect of grammar school attendance on progression to higher education net of the effects of educational attainment holds regardless of pupils' socioeconomic background, suggesting that grammar schools are no better than non-selective state schools as facilitators of upward social mobility.