Thirty years ago it would have been useful to know about whether an applicant's parents had been to university. However, the expansion of HE means that it's not such a great indicator of privilege any more.
Admission decisions need to be made on the basis of objective criteria, as far as possible. Those criteria should be set in a way that does not unfairly discriminate against those from less privileged groups. One implication is that decision makers will have to be more open-minded about candidates' extra-curricular experience - not everyone can afford to spend a year kayaking and volunteering. What about work experience in the family business - how many universities currently acknowledge the value of that?
Where two candidates have achieved the same A-level grades, we believe that reference should then be made to the level and nature of resources that have been used to get those grades. To get a given level of grades with fewer resources is an indication of greater ability and greater potential. In tie-breaker situations this policy would rightly favour applicants from state schools. For a tie-breaker between applicants from two state schools, you'd look to factual information about the average grades being achieved by those schools. Average GCSE grades from the secondary school would be a much better basis for comparison than A-level grades from the sixth form or college.