Quote: The Motor Cycles (Protective Helmets) Regulations 1998
Protective headgear
4.—(1) Save as provided in paragraph (2), every person driving or riding (otherwise than in a side-car) on a motor bicycle when on a road shall wear protective headgear.
(2) Nothing in paragraph (1) shall apply to any person driving or riding on a motor bicycle if—
(a)it is a mowing machine; or
(b)it is for the time being propelled by a person on foot.
So if you're pushing it, no, you don't need to wear a helmet.