From a quick search on the net it seems there are three plausible explanations for the 'daft as a brush' expression.

1) brush of a fox = soft and soft = daft in North England
2) small children dropped down chimneys instead of a brush often incurred head injuries.
3) when a wet brush is poked, you 'dab'. When a dry brush is poked, you 'daff'. These words are onomatopoeic. The word also appears in the first verse of The Flowers Of The Forest, where in context it means something like a nudge in the ribs. When a brush has been daffed a great deal, its bristles splay out in all directions. The brush is then called "daft" and it becomes practically useless. Someone who is daft as a brush is unable to direct their concentration properly to the matter in hand.

No. 3 is the most plausible to me.