The term 'dredging'

[Morning Glory]

The OED has two definitions of "dredge". The first refers to dredging a river, seabed, etc. in search of shellfish, oysters, etc. The second is to sprinkle flour/sugar/cocoa on top of something.
Personally, I think the BBC got this one wrong. All the origins of the word go back to middle English, old Dutch and even Norse words for dragging the bottom of a river, etc. to remove items.
However - it seems to be common (British) English usage for sprinkling sugar or something else on to a cake, biscuit, etc.

In etymological terms you are correct. But this is word usage and the term dredge is certainly used in the UK to mean dusting. A 'dredger', is the culinary term for a utensil with holes for shaking flour or sugar over food.

 

[Morning Glory]

See also, dredging. Cambridge dictionary.

dredge verb [T] (FOOD)​

to drop flour, sugar, etc. over food:
Lightly dredge the cake with icing sugar.