In a sense, this question might have been asked in the "Short answers to simple questions" thread, and I hope the mods will forgive me for answering it relatively briefly. There is one resource above all that you need to read, though it is neither an easy nor a straightforward book, and that is Patrick Wormald's acclaimed and game-changing The Making of English Law: King Alfred to the Twelfth Century, volume 1 (2001).

Unfortunately Wormald died before he could complete the second part of this planed two volume study, but it was a life's work, and the part he did finish up is central to pretty much every discussion of Saxon and Anglo-Norman law that has been held since 2001.

Broadly, Wormald argues for a legal system that was, at its core, an oral one that proceeded from the personal authority of the king in person. This sets him against his Oxford colleague James Campbell, who argued that lay literacy, and hence the written word, was key to the strength of the late Anglo-Saxon state.

For Wormald, however, the evidence for ‘pragmatic literacy’ and lay literacy in C10-11th England is limited. He questions both the status and the function of written Saxon law codes, and sees Alfred’s famous Domboc not as a practical document, but rather as an expression of ideological aspirations. Similarly, Wormald treats the written "law codes" that survive for the C10-11th as mere “minutes” of “oral decrees”, kept for the use of the minute takers (usually churchmen interested in asserting privileges and land rights) – that is, he disputes that these “codes” had the force of statute law and instead sees them as ecclesiastical records kept for the purpose of buttressing potential future claims. In defence of this position, he points out (incontrovertibly, though interpretation is another thing) that there is no instance of any part of any Saxon law code being cited in any legal case we know about, and that we have no "well-thumbed" copies of Saxon legal codes that have indisputably been consulted to help resolve contemporary disputes that actually came to court.

Thus, for Wormald, it was the verbum regis – the word of the king – that gave a written text the force of law. From this perspective, we can anticipate he would have argued, in his second volume, that there was indeed a fundamental change in legal systems as Saxon became Norman England, and that – certainly by the Angevin period – written law had assumed a more central position in legal discourse.

If you want to go beyond this first-step suggestion I would suggest looking at the companion volumes written by Loyn and Warren in the Governance of England series, Loyn's The Governance of Anglo-Saxon England, 500–1087 (1984) and Warren's The Governance of Norman and Angevin England, 1086-1272 (1987). Both are quite old, but historiography doesn't move all that fast in these fields and each is still useful.