Cheers for the reply.
It is indeed the right way around, and it does have 5V at its input and is grounded. I've doubled checked everything, and have also bridged the two bits of track that have to be bridged according to the assembly guide (was a bug in the PCB artwork).
I checked the output of the second regulator and while it isn't 4.75V, there is a voltage of about 0.1V across it - combined with the fact it gets very warm - would that suggest I've got a short somewhere creating a very large load for the second regulator to drive, hence the low voltage and high heat output?