Blackstone's Commentaries: Book 1, Part 1, Section 3
http://www.constitution.org/tb/tb-1103.htm
But the irruption and establishment of the Danes in England, which followed soon after, introduced new customs, and caused this code of Alfred in many provinces to fall into disuse; or at least to be mixed and debased with other laws of a coarser alloy. So that about the beginning of the eleventh century there were three principal systems of laws, prevailing in different districts. 1. The Mercen-Lage, or Mercian laws which were observed in many of the midland counties, and those bordering on the principality of Wales, the retreat of the antient Britons; and therefore very probably intermixed with the British or Druidical customs. 2. The West-Saxon-Lage, or laws of the west Saxons, which obtained in the counties to the south and west of the island, from Kent to Devonshire. These were probably much the same with the laws of Alfred above-mentioned, being the municipal law of the far most considerable part of his dominions, and particularly including Berkshire, the seat of his peculiar residence. 3. The Dane-Lage, or Danish law, the very name of which speaks it's original and composition. This was principally. maintained in the rest of the midland counties, and also on the eastern coast, the part most exposed to the visits of that piratical people. As for the very northern provinces, they were at that time under a distinct government.[8]
Out of these three laws, Roger Hoveden[9] and Ranulphus Cestrensis[10] inform us, king Edward the confessor extracted one uniform law or digest of laws, to be observed throughout the whole kingdom; though Hoveden and the author of an old manuscript chronicle[11] assure us likewise, that this work was projected and begun by his grandfather king Edgar.
Well, you just blew your own theory, didn't you?
First, you said "Welsh or "British" law wasn't incorporated into English law."
Then, when you took the trouble to look it up, you found that you were wrong.
You also found out that the argument made upstream, that English law is "really" Danelaw, was also false.
Good job!