Who says that they didn't? Robin Fleming argues in Britain After Rome that the idea of the Anglo-Saxons as a purely Germanic culture is misguided and not supported by the evidence that we have available through archaeology. She points to the blend of clothing and jewelry styles that emerged following "Anglo-Saxon" migration to Britain as evidence that these two cultures were assimilating into something difference from either that came before. She views this process as more or less a peaceful one. While they was some endemic violence inherent to the time period, she does not see evidence for the mass violence that is often assumed to have accompanied the Germanic migration into Britain.

However Peter Heather offers another explanation that is worth mentioning. He posits that due to the fragmented and small scale nature of migration into Britain, combined with a fluid cultural identity for the native British there was little reason for the native British to hang onto their culture in certain parts of Britain so the population assimilated into the new Germanic one.

Also worth bearing in mind is that the label of "Anglo-Saxon" as applied to the migrators themselves is misleading. While many of the Germanic people who came to England did come from Jutland or Saxony, others came from Norway, Frisia, Ireland (not even Germanic people!), and Sweden. Also that the process of assimilation was not as smooth in some of these places as you might imagine. For example, Frankish Law (or Salic Law) maintained legal distinctions between Franks and Romans for centuries following Frankish control over northern Gaul. Even though the populations "assimilated" in the end, we should not imagine that this process was quick, easy, or assumed.