I can't comment definitively because I haven't studied any economics whatsoever. However, my gut feeling would be "no".
It probably makes more sense to talk in terms of a law degree, since I'm a law graduate and corporate law is primarily law but with an economics-based twist. One would expect a law graduate's degree to be the "most relevant" to a career as a lawyer.
Firms tend to use academics as an autofilter; if you don't have AAB at A Level and a 2.1 or above your application might not even be looked at by a person. However, in the context of corporate law I don't believe any weighting is given to particular subjects. Your 2.1 is evidence of your academic ability and your hard-working nature, regardless of your discipline.
We then get into the open questions on the application form, where your writing ability and soft skills show through. At this point the firm is most interested in your commitment to a career in law (they're about to make an investment in your future so they want to see an informed decision!), your ability to express yourself clearly, and sometimes your understanding of the wider business context in which the law operates.
At interview, these skills are tested in more detail, with more in-depth commercial awareness exercises and a general assessment of your "fit for the firm" in terms of its culture and ethos and your particular strengths.
At no point was I required to show detailed knowledge of the law, even though practising solicitors will be using the law every day. Similarly, I suspect that the level of detail in your economics degree far exceeds anything that would be expected at interview. I was applying for TCs in summer 2012 and the only vaguely economics-related content I was expected to understand and explain the basics of interest rate swap misselling/LIBOR (especially since I'd mentioned work experience focusing on those areas in my CV) and the Eurozone crisis.
I can certainly call in Freshfields' graduate recruitment for a second opinion, although I'd hope that I'm not too far off the mark!
If you have anything to add to the above, Jess, I'd be interested to hear it. Thanks.