Non earthed back box & metal faceplate

[Mildcheese]

I'm in the process of changing my plastic faceplates to chrome.
The light switches seemed easy, metal back box had an earth wire connected to it already, I then connected a 'fly lead' (not sure that's the right term) from the chrome faceplate to the same earth point on the back box.

The sockets also have metal back boxes but the earth wire doesn't connect into it, instead it goes into a terminal on the back of the existing plastic faceplate.

My question is, how will the new chrome faceplate be earthed, it seems pointless me connecting a fly lead to the back box when the back box has no earth? Do I need an earth wire from the faceplate to connect into the earth terminal on its rear?

Thanks