Thank you and sorry, I'm a bit confused when you say all three earth conductors as I only have two (first picture)? There's the earth coming out the main cable and then the other one that goes to the box. Should there be a third earth cable?
I need to replace this double socket, but the replacement is slightly different to the old one and not sure if I need to add a new earth cable going to the box please?
Here is a picture of the existing socket that needs replacing:
and here is the new socket: