So recently when I went ingame I noticed my fps hovering around 20. It's ridiculous, I thought, I have no other applications open and my laptop is good enough to run Bioshock Infinite on high settings. I thought maybe it's because I'm under-clocking my GPU (it was custom set when I bought it but I lost the values and it's reverted back to default).
Anyway, I noticed that Google Drive was running in the background, so I closed it, and BAM, 60fps, flat. I have no idea why - maybe it's to do with Drive doing some sort of constant reading of the hard drive, but it completely fixed the problem.
So if any of you are suffering from low FPS, and you have Google Drive running, try closing it.