Black potatoes.

Can somebody help me determine what is wrong with my potato crop. My entire crop of King Edwards has either, when cut in half, started going black in the middle or is starting to rot on the outside. Looking at it's foliage, nothing untoward appeared to be wrong, aside from where the slugs had dined, but upon digging the tubers up I started noticing problems. Can I blame slugs, the excessively wet weather or is some other factor responsible (don't let it be blight, i've still got my reds in the ground). Any assistance given will be gratefully recieved.

Sounds like soft rot.  Are the tubers smelly?

I don't think there's anything you can do about it now and I'd get your reds lifted sooner rather than later.   Found this on another site which may help:-

Rotten tubers. Bacterial soft rot enters tubers wounded by tools insects or disease. The vascular bundles in leaves, stems, and tubers turn black and bad smelling. Rot can not be cured. Plant potatoes in well-drained soil. Remove and destroy infected tubers. Remove all plants and plant debris at the end of the season. Promote good drainage by adding aged compost and organic materials to planting beds. Avoid over-head watering. Rotate crops.

Sulfur applied to the garden may reduce rots. Protect tubers from injury.