Abstract Among the significant inequalities within Britain’s school system, the greatest lies in the resources gap and the social segmentation between fee-paying and state schools. Published estimated average effects of attending private schools in Britain on academic performance are modest, but nevertheless significant at each stage of education. Cumulatively, by the end of a school career the private school pupil has gained notably higher qualifications compared with a state school pupil with an observably similar background—enough to ensure a distinct advantage in access to a high-status university, a good job and high pay. These gains add to the educational advantages of growing up with an affluent family background. An unusually high proportion of private school alumni occupy highly influential positions in business, in the judicial system, in the press and in politics. A further financial advantage from private school stems from an increased probability of partnering with a richer spouse. The hallmark of a good school policy for reducing inequality would be one that opens up access to private schools, so that participation is no longer constrained as much by financial background, and diminishes substantially the inequalities between schools’ resources. Feasible reforms are of two kinds: those that would lower parental demand for private schooling, inducing enlargement of the state sector, and those that would directly integrate pupils from the state sector into currently private schools. Currently, bursaries are far too small to make a substantial difference.