"I did it so it isn't impossible"
Not really convincing. How many poor kids did not even come to an understanding of how the admission system works? How many kids did not even know what work was to be put in?
I am also someone born at the bottom (my first passport was a convention of 1951 passport), who went to a world famous university. As I've gotten older, I've realized it's not really a useful way to think about it. We like to say "you can do it if you really try", but it's just not true. Not only is it not true, it's a thought-ending statement that makes it easier for rich kids and harder for poor kids, because why would you need to support the poor kids if they can just work really hard?
Even you have to be able to see that you got lucky. When I applied, the entrance rate for my course was about 8%. I had no idea that I could have tried easier courses, or that I could have filled the form in slightly differently for a better shot. A single-digit acceptance rate is a lottery. You could do everything the same again and not get in. You don't realize it when you get in, because you happen to get questions that you can answer, but there's a heck of a lot of questions an Oxford professor can ask an 18 year old that will make him look bad.
When I arrived, of course all the other kids were ordinary upper middle class kids. People went to feeder schools where they teach you how to do the Oxbridge interview. People who didn't grow up pinching every penny. What happened to the poor, hard-working kids? They're mostly not there.