Can a motorcycle brake like a car?

It might be true. Even if the handle is down, the cable might have frozen (rusted) in the on position. Also check for jammed calipers, the last time this happened to me I had both front brakes...

Hard work with people beeping you and driving you like stupid!

Well before you go out and get factory brakes i wood try and pump your brakes before you going driving the car, pump at least 10 times or more to be safe.

The rear brake pedal is under your foot on the right hand side and the front brake is a lever on your handle grip on the right hand side.