Much of the heavy lifting on widening participation in higher education to date has been undertaken by newer and less selective higher education institutions. The access challenge therefore remains greater at more selective institutions. They could learn from the best practice that exists in less selective universities. It will take nearly a century for highly-selective universities in England to raise the participation rate for 18-to-30-year olds from the least advantaged areas to the existing participation rate for 18-to-30-year olds from the most advantaged areas. If, instead, the number of degree places at more selective institutions were kept steady, the number of places for advantaged pupils would need to fall by as much as 10,000, which is one-third of current annual intakes. Failing to find ways of expanding university places will prompt acrimonious battles over who secures degree places -- there will be a clash of the classes. Universities in England should produce two published offers for degree courses: a standard entry requirement and a minimum entry requirement, of up to three A-Level grades lower across three A-Levels (so BBB compared with AAA, for example). Universities should also consider using random allocation of places for students over a certain minimum academic threshold (as has occurred in other countries). The Office for Students should challenge highly-selective universities to expand student numbers in innovative ways to diversify intakes, including degree apprenticeships, foundation years and courses for part-time and mature learners. Social mobility rankings for universities should be established, measuring outcomes for disadvantaged students. Universities should undertake a social mobility audit, benchmarking their work on outreach, access and academic and pastoral support for disadvantaged students.