The process of conversion in Anglo-Saxon England was mostly an elite-driven process. Missionaries, like Augustine, were at first successful in converting powerful Kings who could help protect the church but often times these successes were diminished by the King dying. Eventually in 634 Oswald who was King of Northumbria helped set up the Lindisfarne Monastery. The power of the Northumbrian dynasty helped to spread christianity further south in England.

Understanding how much of the population in England converted is slightly more challenging, but here we can turn to archaeological evidence. By the 8th Century you begin to see burials organized around local churches, new orientations were used for burials (west-east) and less grave goods. All of these are distinctive marks of Christian burials. Of course it is hard to tell how strongly people believed in Christianity, compliance does not equal conviction, and archaeological evidence can only shed scant light onto how intense Christian beliefs were. In earlier decades we can see the mixing of pagan and Christian beliefs in burial evidence. Continued usage of older burial sites, but with the new west-east orientation is one example. We also still can see pagan burial items well into the 7th and 8th Centuries implying that the older beliefs people held were not being completely overwhelmed or abolished.

It is also true that many of the Britons who were living in England before the arrival of the Anglo-Saxons may well have already been Christian and there is evidence of continuity of belief in certain places in England. Being conquered by a pagan king may have eventually overwhelmed the older Christian beliefs, only for them to be brought back later in time. Again the arrival of a new belief was not a guarantee that the old would be completely forgotten, and it is likely that people continued to hold onto to their pagan beliefs in new Christian regions and vice versa.

Hopefully this helped!! I'm pretty tired while writing it.

Pretty much every time when you read that such-and-such nation converted to Christianty it means that the king, his court and highest ranking aristocrat became Christian, not the entire population of the nation. For example, look at Poland, the nation officialy became Christian in 966, yet in 1038 pagan population was so big that it was able to form a major revolution.