About 50% of people on the LPC at least didn't do Law at university. I don't know about barristers, but for solicitors it's not a problem at all. In fact, if you've done something like a language or Economics then it might well put you at an advantage as you'll have other skills that you can bring to the job.
But the bottom line, it will affect your career opportunities in any big way, especially not with a degree in economics.