I would think that it's not so much what the vehicle looks like (although that would be part of it), it's more what he is purporting or holding himself out to be something that he isn't that is the greater problem...!!!
You got it in one straps!!
It is illegal to hold yourself out to be a member of CFS / SES / MFS if you are not such.
While I haven't read the case law on this, I would expect that you wouldn't have to actually say "I am a member of the XXXX service" in order for it to be illegal. You could have to look at what impression people get by your behaviour - that may be enough in court for you to be found guilty of impersonation.
As for badging on your private vehicle - I haven't looked at the specifics of that under the Regs, but the issue of the impression it gives to members of the public as to who you are / what you do, could contribute to the impersonation issue above.
As for the issue of a GRN...... I wouldn't think it is illegal for you to have a GRN radio in your vehicle, if you were not an member of the emergency service (after all, for a while, they were installed in vehicles belonging to Council fire prevention Officers) - but you would have to be officially sanctioned by a specific service to have one.
Pip