With a little more digging I found the in-game performance overlay, which appears to show the potential frame rate for the GPU and CPU independently. In my case the CPU FPS is lower (and tallys with the actual FPS), suggesting that the CPU is the limiting factor.
My CPU usage is between 50% and 60% however. I was under the impression that would be higher if there was a bottleneck. Could it be the temperature (around 90°)? Is there something else I'm overlooking?
One other anecdotal thing I've come across, which sounds mad, but I'll mention it. I've seen some people report that either turning on or off the EA overlay makes a difference in this situation. Probably a coincidence, but for what it's worth it does seem I get a 20FPS bump if I turn the overlay on.