Considering the theme of equal opportunities companies (purport to) care about, is mentioning that I am the first person in my entire family to go to university a bad idea? It leaves a bad taste in my mouth, but it's tough out there and you have to use what you have to get into an industry dominated by Oxbridge grads.
Your cover letter’s job is to get you the interview. Your pioneering educational effort shows perseverance and courage, as you know.
Can you make the case, briefly, in your cover letter that your perseverance and courage will benefit your employer and their clients? If you can do that, definitely do!
All the best to you.