Related: Carl Shulman's How hard is it to become Prime Minister of the United Kingdom?

From what I've heard, Cambridge EAs have already been elected to positions in the Cambridge Union. I think several EAs at Oxford have also been in Oxford Union-adjacent circles, although it seems like most haven't engaged with the Union due to lack of interest.

FWIW, I'm guessing most people focused on a social science at Oxbridge have already made up their mind about whether they'd like to network at the Unions or try their hand at getting elected for something. That being said, it seems like relatively few people have considered the potential impact of voting in said elections, as well as other things that would not require serious engagement. 

Other than the first Guardian article you reference, I would also recommend this piece and the book it is about: https://www.theguardian.com/books/2022/may/01/chums-how-a-tiny-caste-of-oxford-tories-took-over-the-uk-by-simon-kuper-review

It made the potential political impact of the Oxford Union much more salient and clearer to me. Talks about a range of things like the history of the Union, political connections, debating styles, the inception of Brexit.

Maybe it should also be mentioned both Student Unions are also likely high impact opportunities.

https://en.wikipedia.org/wiki/Oxford_University_Student_Union#List_of_Presidents_and_Executive_Members

https://en.wikipedia.org/wiki/Cambridge_Students%27_Union#Former_Officers