Is there a specification or a general rule as to how far away an
outbuilding can be before it requires it's own local earthing
arrangement? I've looked through past posts but couldn't find
such a figure mentioned.

As I understand it, you'll have to ensure the earth loop impedence is within
spec, which gets increasingly difficult with longer cable runs and increased
power. Also, you have to run main equipotential bonding back to the earthing
terminal by the consumer unit in UNBROKEN thick earthing cable. This is an
issue if you have metallic services, or structural metalwork.

Christian.