Thanks so much for the helpful guidance. It has given me a great deal to think about. Particularly Peter Donis who went to so much trouble to show me I was wrong! This is not a mistake that I will make again.
"That distance is indeed an invariant, and with appropriate choice of coordinate system we can calculate its invariant value at the event horizon and anywhere except at the central singularity" - precisely. I calculate the distance in Schwarzschild coordinates and it comes to infinity and hence...
I have read that before but my question is how do I square it with D (the metric 'distance') being an invariant? You cannot get rid of it if it is invariant.
It seems to me that the Schwarzschild singularity is generated by the metric function which is an invariant and so has the same value in any coordinate system, so why is it not equally valid?