Sparrow - yep I noticed that once I'd got through the hard skin it bit in and cut cleanly and with satisfying spirally swarf.

Thanks all.
I'll give it a go first by making a drill sharpening rest for my bench grinder - I've nothing to lose as I can't make them any more unusable.
In truth, now that I've finished my immediate drilling needs I probably won't do anything to the duff bits until I need to drill some more holes and then I'll go through the same old process of grumbling, faffing and searching through for a sharp drill all over again. Sigh.
('Twas ever thus).