Most reforms at Oxbridge have been imposed from outside by government. I have a radical plan.
The first thing is both universities are constrained by a physical inability to expand. I would create a University of Chelmsford and send Anglia Ruskin packing from Cambridge. Likewise the University of Reading lacks critical mass. They can have the academics, the courses and the students but not the buildings from Brookes.
Both Oxford and Cambridge should each create two new undergraduate halls; halfway to being independent colleges. Both universities should be set a target of achieving the same number of home undergraduates of both sexes as the number of home males they had, immediately before the men's colleges went mixed. Put the new colleges and extra accommodation for the other colleges on the Ruskin and Brookes campuses.
Each university should offer degrees with an integrated foundation year so as to be eligible for student funding in the ordinary way. Run a residential selection exercise during the long vac in the middle of VIth form based solely on potential. Put geographic & racial quotas in place for spots in the selection exercise and limit the spots to pupils of target schools but do not create quotas for university places.
Where is the money coming from? Effectively from the universities and their fund-raising capabilities. The universities do not have a right to insist that somehow students are some sort of additional burden. I get rather annoyed when Oxbridge claim they subsidise undergraduate teaching. They are educational charities, It is rather like Guide Dogs for the Blind complaining it has to buy dog food.