To be honest, recruiters are no paying that much attention to the cover letter.
In terms of the structure I would use the following (in paragraphs):
- Intro of who you are
- Why you (several reasons)
- Why "The Company" (Usually 3 reasons)
In terms of the content:
Why you is about your career path and extracurricular activities. Depending on your experiences either start from the first or from the last role (the later you are in your career the more sense it is to start with last one). You can mention a couple of your unique selling point and structure your lifepath around it. Add memorable projects or experience with high impact / cool brands / etc. that will stay in the memory of the reader.
Why "The Company" question can include the following arguments:
- Brand / positioning / market share in the region
- More clients / projects / expertise in the industry you are interested in
- More well-known stories of success in your city
- Your friends working there
- Your interactions with the other consultants before the interview
- Your prior experience of working with the Firm on a client side
- Office traditions
- Work experience with firm alumni