Do you have to wear a bike helmet?

Just wondering if it is a legal requirment that one must wear a helmet when cycling on public roads.

No it's not a legal requirement:
"As a cyclist, you are a vulnerable road user and your bicycle will not protect you if there is a crash. The law does not require you to wear a helmet. However, in the interest of road safety, and in your personal interest, you should wear a helmet at all times."
See below :

No, but, imho, anyone cycling without a helmet is stark raving mad. I recall hearing, some time ago, that non-helmet wearers are at something phenonemanally greater risk of serious head or fatal injury, around 85%, compared helmet wearers.

A quick google came up with the stat of non-wearers being 14 times more likely to be fatally injured.

I hate to see parents allowing kids cycle with helmets slipping down the back, as if to protect the back of the head, very often leaving foreheads totally exposed. While there is risk to the back of the head, trauma is more likely to the front.