A suburb of Redditch in Worcestershire is called Headless Cross. Does anyone know the origin of this name?

Not exactly, though it's a name found in a few parts of England, sometimes as a street name. One explanation is that it derives from the pre-Reformation practice of using a headless cross to mark the boundaries of church land and that kind of thing.

Nearby Bromsgrove however has a suburb called Lickey End (I kid you not), and I have no idea how that came by its name.

Thanks - that sounds a plausible explanation and will do nicely to shut up the questions from the back seat when we drive past the road sign.

We don't drive through Lickey End - I am quite pleased about that, really!! :-)