Hmm...whereas the Celtic tongue certainly fell out of vogue amongst the conquered Britons under Anglo-Saxon kings, Latin continued to be immensely important in Anglo-Saxon Britain for its obvious administrative utility. In fact, it was the preeminent written language of administration and law in that realm at that time, with documents written in Old English coming in at second place. Bede, for example, being the ecclesiastic man that he was, wrote his landmark history in Latin. It was expected that his learned Anglo-Saxon contemporaries would understand it effortlessly. Of course, it was no longer the common tongue, but like elsewhere in Europe it was the language of high culture and the educated elite.
I assume you already know this.
However, it's a good reminder for any n00bs lurking here who aren't familiar with the Middle Ages. Hell, for that matter, Latin remained the preeminent language of communication across Early Modern Europe even while French nipped at its heels in aristocratic circles.
@Clandestino: that map of Y-DNA haplogroups is fascinating and revealing for so many reasons. Look at the difference not only between northern and southern Italy, but also the similarity of southern Italy and Sicily with Asia Minor (i.e. Turkey). Aside from most of England, Western Europe (including the Isle of Corsica and the Balearic Islands) is one big solid chunk, while Germany is a giant hodgepodge of different genetic influences as I've always suspected. I'm actually surprised to see only the northernmost part of the country as being significantly impacted by Nordic genes. It seems like I1 (Northern Proto Europeans) and R1b U106 (North European Eurasians) are very mixed in northern Germany, Denmark, and the southwestern Norway and Sweden, but that "true" Germans are the North European Eurasian type, by way of covering most of the territory of what is now Germany (plus the Netherlands).
If one is to fully trust this map and population survey, it would be pretty clear to see England's obvious genetic link with both the I1 and R1b U106 types found in Germany and the Nordic countries. However, as it should be expected, this heavy Germanic influence is mixed with the original population of Britons. I think the Britons living under Anglo-Saxon rule adopted their Germanic tongue not only because their new rulers spoke it, but also because a significant amount of their new neighbors and those in positions of authority also spoke it. In that case, it is clear to see the advantages of adoption over sticking to a Celtic language that didn't allow you to advance up the social ladder.