Bernard Cornwall made the claim in his anglo saxon series of novels.
Also, what was the punishment for killing your own slave?
This may be a slight exaggeration, or at least a mild warping of the truth. While the Laws of Alfred do state that the killing of slaves is illegal, it is perhaps disingenuous to state that Alfred is the first to actively outlaw this.
Slavery under Anglo-Saxon law is a slightly vague concept, but slaves do have a variety of legal rights and protections under various English laws. In the earliest English law code, of Æthelberht of Kent, all killing not in self defence or defence of property is outlawed, and separate punishments are stated for those who attempt to rob slaves or steal another's slave. Under the West Saxon laws of Ine, it was forbidden to sell an English slave overseas, a marked contrast to earlier Kentish law in which a thief caught in the act could be sold overseas into slavery as a punishment. Slaves could also not be ordered to work on a Sunday, even if they themselves were not Christian. The killing of other people's slaves, therefore was definitely already illegal, and it seems implicit, at least under Kentish law, that to kill one's own slave is similarly illegal, but we could surmise that weregild would be liable in this instance to the king. These protections are then somewhat extended in Wessex.