I think I know the bad news here but thought I would post it to be sure. What makes me doubt is that it has only affected 3 out of about twenty bulbs; the rest are a good size and clean. They are growing in sandy soil and were not mulched and not watered much apart from the cold and rain we had early on.
Could it just be these three have rotted off in locally damp soil whereas the others were ok, or is it definitely white rot in which case this is another place I have to add to my map not to plant alliums.
The pohoto shows left to right getting worse.