Looking through their resources the important images are all Jpegs, so I would have thought the overly compressed JPEG@2x solution would work for them. I also see a few individual PNGs, some of them individual icons, the other sprite sheets. Perhaps they'd be better off using webfonts for icons, or Base64 encoding images into the sprite sheets with SASS.
My gut feeling is that this solution might be more complicated than the problem.
BBC News does use webfonts for icons. The examples you see on the Imager.js Github repository are not exactly what BBC News uses in production, consider those as guidelines for using the plugin.
I was looking at the resources on the actual BBC news website. My point being, I wonder if the BEEB might be better off using webfonts for icons since every other image can be a jpeg. And if it can be a JPEG, the aggressive compression technique might be a better approach since it doesn't require any JS or additional HTTP connections.
Are you saying that the BEEB has a policy of not using web fonts? If so, why?
My gut feeling is that this solution might be more complicated than the problem.