Extract from OED Online

brush, n.²

SECOND EDITION 1989

ADDITIONS SERIES 1993

Add: [I.] [1.] c. In colloq. phr. as daft (mad, etc.) as a brush, quite daft or mad; crazy.

1945 H. WILLIAMSON Life in Devon Village 12 'Mazed as a brish,' declared Mrs. 'Revvy'... 'I reckon he's not all there.' 1974 P. WRIGHT Lang. Brit. Industry xiv. 129 'As daft as a brush' (which flops, unable to stand upright). 1980 J. O'FAOLAIN No Country for Young Men vi. 136 She's as mad as a brush. Thinks she's privy to secrets of national importance.