Just to add on to this, financial circumstances don't only affect university choices but also what you can do at uni and the ways you can improve your CV.
I am first gen uni, state-school, etc, and to got into a RG. However, at said RG, I would have loved to do one of their year abroad options. Unfortunately, the cost of living was higher in the areas where I would be able to do this, so I had to give up on that hope as my family and I would be unable to afford it. People from more fortunate backgrounds could afford this and become more desirable to law firms as a result.
So, I do think it is important that account is taken of certain factors - including socio-economic ones - as some people just can't access the same opportunities as others.