Afaik Oxbridge dropout rates are well below the national average. Have no personal experience of how unis handle MH issues, but dd1 has had an 'educational' (i.e. no meds!) diagnosis of ADHD whilst at Oxford, and their provision has been really good imo - she has not used it fully, tbh, but that's not because the support hasn't been offered. Her college have also looked after her 'college son' who has Aspergers/HFA very well.