William the Conqueror certainly didn't "abolish" slavery in any explicit or outright way, if that is what you mean. He also, it can be said, didn't abolish it "indirectly" in any personal or "active" sense. In other words, William, qua William, had less to do with the disappearance of slavery in England than the raft of socio-political changes that came with William. But even here changes in slave-holding practices are visible in England a good century before William and his Frenchmen show up.

The shift from slavery to "servility" not just in England but throughout Western Europe is one of those major medieval topic that resurges every generation and is a fairly hot button issue.

The book to consult is David Pelteret's Slavery in Early Medieval England

Pelteret does an excellent job of really deeply digging into what defines a slave as a slave and the ways in which the various legal, economic, political, religious, and social circumstances behind slavery changed between the ninth and the twelfth century.

Obviously the Norman Conquest (as I noted above) had a major impact on all of these circumstances, but it was by no means the sole actor in the shift from Anglo-Saxon slavery to Anglo-Norman/English medieval servility.

Already before the appearance of the Normans we can observe a slow growth of manorial practice in England with the attendant servility that comes with it (things like work obligations). Freemen were becoming tied to the land and at the same time we see an ongoing interest in manumission (freeing of slaves) brought about probably both for economic (for instance it is cheaper to let serfs feed themselves and support their own family on land that you own than to provide for them actively) and religious reasons (i.e. it is spiritually beneficial to free slaves).

It is also worth noting that as England became more and more unified and "pacified" the central producer of new slaves, i.e. warfare and conflict, thus also began to wane.

What the Norman Conquest does is effectively speed up a process that was already taking place as England became more and more influenced by Roman (i.e. continental) law and by continental land holding practices. The institution of entirely new land holding practices and legal practices per-force across the whole of England rapidly transformed the already waning practice of slavery. As Pelteret puts it, it was a "shock to the body politic." By the year 1200 slavery was essentially gone in England, though of course servility continued.

To give you a quick summation from Pelteret's work:

What seems with the hindsight of centuries to have been a dramatic social change took place without comment from the people of the age. The multiplicity of forces at work and the gradual nature of the social transformation must provide the reasons for this. The decline of slavery in England was the product of a combination of impersonal economic forces, purposeful human action, and chance. (258)