Is this JB safe?

[flameport]

As a possible alternative, could another JB be added to the FCU output (which is earthed) before the bathroom switch.

Yes, but only if that FCU really does have an earth that's connected.
The existence of the earth wire doesn't mean anything on it's own - it must be tested to ensure it's properly connected back to the consumer unit earth terminal.

I’m assuming I can’t do this work myself under regulations.

No regulations prevent that or any other electrical work.

 

[Simc101]

Yes, had the cover off earlier and it’s earthed, they just didn’t bother on the junction box end

 

[morqthana]

Yes, had the cover off earlier and it’s earthed

Have you

tested to ensure it's properly connected back to the consumer unit earth terminal.

 

[Simc101]

Sorry, that was in response to Morqthana.
I can only assume it’s genuinely earthed, being a ring spur, and the ring appears to be earthed from the sockets I’ve seen.
Can I look at the CU for that circuit to confirm or is testing the only way? I wouldn’t know how.

 

[Ragnar_AT]

Sorry, that was in response to Morqthana.
I can only assume it’s genuinely earthed, being a ring spur, and the ring appears to be earthed from the sockets I’ve seen.
Can I look at the CU for that circuit to confirm or is testing the only way? I wouldn’t know how.

Testing is the only way. Not a real DIY job as it involves opening the CU and testing between the earth bar and the wire at the FCU.