Most big law firms tend to have a 50-50 intake between law and non-law trainees. I have an acquaintance at White & Case that did her undergrad in Economics and then the GDL. Ideally, you should focus on the Banking/Capital Markets/Corporate law firms who tend to make their money in finance (there are a lot of those!)
It's definitely possible, but your background, where you got your Economics degree from, how well you network. All of that makes a huge difference as well.