Is this the 'Stephen Lawrence' Diversity scheme? In any case, I personally think the best way to approach the cover letter is to either show you academic brilliance OR your involvement in Extra-curricular activities (volunteering or positions of responsibility) OR BOTH.
From my understanding, the Diversity Access Scheme is for those who are academically capable but their surroundings/background prevents them from aiming high. As such, the scheme aims to target such people amongst others.
Cover Letter
Depending on whether there is a word limit for the cover letter, I would try and have a logical structure, i.e., (1) introduce yourself, (2) reasons on why they should select you (Back up any reasons with your experiences), (3) perhaps what diversity means to you etc...
If you have met or know anyone at
Freshfields make sure to include the encounter you've had with these people. This always seems to help.
CV
Again its best to keep it 1 to 2 pages max. Make sure you list your experiences, avoid typos, make sure the format and font is consistent throughout, be concise and try to breakdown any long paragraphs.
I would recommend the following format:
(1) Education (I will usually include a breakdown of my marks & grades)
(2) Experiences (I usually have a subsection for Legal experiences and Work experiences)
(3) Extra-curricular Activities
(4) Prizes/Skills/Languages etc
Goodluck!