Here’s a chart that did the rounds last year, showing the chance of getting into elite US universities, such as Harvard, by parental income - after controlling for test scores:
By using the UCAS admissions data as a whole you are not discriminating between different Universities. I suspect that if you separated University admissions into groups: Oxbridge, the Russell Group, and Million+, you would find quite a difference between admissions by quintile to the different groups. In particular, I suspect that you would find proportionately more from the lower quintiles going to the Million+ universities. If you can do this, it would be an interesting exercise.
By using the UCAS admissions data as a whole you are not discriminating between different Universities. I suspect that if you separated University admissions into groups: Oxbridge, the Russell Group, and Million+, you would find quite a difference between admissions by quintile to the different groups. In particular, I suspect that you would find proportionately more from the lower quintiles going to the Million+ universities. If you can do this, it would be an interesting exercise.
I suspect you are probably right!