Personally, I think that personal branding is becoming more and more important. This means showing the employer more of you and your character. 

One way you can do this is by not undervaluing your non-legal work experience; it is a great way to showcase key transferable skills including adaptability to new and high-pressure environments. Law firms will be looking for a wide range of attributes that can be illustrated through varied experiences, not just in the arena of law. There's loads more on this and how to practically implement it in your CV here.

Hope that helps!