I don't know the name, but I noticed there are two different types of plants available in garden centres. I have both.
Type 1 Bulbs small, elongated, easily dividing into two. Plants smaller, up to 10 cm, 1 or 2 flowers per stem. Flowers up facing, the biggest of all chionodoxa. Often not clear blue, somewhat purple tinted and not dark.
Type 2 Bulbs bigger, round (like Scilla sibirica or small Hyacinthus orientalis), without visible tendency for division. Plants bigger, ca 15 cm, 2 to 5 (or more) flowers per stem. Flowers up and side facing, big but smaller than type 1. Within this type pink and white clones are sold. The blue clone has clear dark blue flowers (with white eye, of course).
Both plants retain their different features in mixed garden population. Shaun, your plant rather belongs to type 1
And the plant sold by The Pottertons as C. sardensis is clearly different - like an intensely dark-coloured type 2 miniature.