I did the same as you but for solicitors,
I just did my CV and wrote something along the lines of,
Please find attached a copy of my CV for your consideration. I am currently studying ... and wish/have applied to ... to study ... .
I would very much like the opportunity to be able to complete some work experience with you and would appreciate it of you could considere my application.
Thank you for your help
Kind Regards
....
Something along the lines of that, thats all I did, I don't think they want to sit and read a 10 page long letter and most places ignore you anyway. Well I found this with Law firms
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