Ok so.....

The Welsh were not Christianized by the English, but that is neither here nor there. I'm going to focus on the Christianization of the various kingdoms in England that were dominated by a mix of the Angles, Saxons, and Jutes AND native British populations following the collapse of Roman authority in Britain. If you're more interested in the Christianization of the Roman province of Britannia, well I can't really help you very much there.

So in the aftermath of the Roman withdrawal from Britain the native Church essentially withered on the vine and was replaced, or at least supplanted, in the lowland areas of the island by the germanic pagans from the mainland/Scandinavia. Christianity however survived in the highland areas of what is today Wales, but in England for a century or so Christianity was in retreat. Robin Fleming proposes that the native British Christians assimilated into the new comers culture and way of life and became Anglo-Saxons in those parts of the country conquered by the new comers. Christianity in these contexts lost its cachet and prestige and fell into decline in England.

This changed in the late 6th century. Our only textual source for this time period is Bede's Ecclesiastical History, and he tells us that the Papacy dispatched a mission to King Æthelberht of Kent and received permission to establish a church in the kingdom. His Frankish wife was also a Christian, and it seems that eventually the Church made significant headway in converting the population and eventually the King himself converted.

In the rival kingdom of Northumbria however the impetus for conversion came from Ireland and the famous monastics from the Emerald Isle. Bede spends a good portion of his narrative fanboying over Aidan, an Irish monk and later bishop, who went around England performing miracles and living a saintly life. He eventually formed the core of the church in Northumbria, including the famous monastery at Lindisfarne. Pressure on England from both Ireland and the continent was responsible for bringing Christianity to England. According to Bede however, the native British Church played little role in bringing Christianity back to England, he might be underplaying their importance though due to his biases against the native British.

However this process was not a simple narrative of progressive Christian success. Paganism did not die quietly in England however. Kings such as Rædwald in East Anglia and Penda in Mercia were able to maintain hegemony over numerous other kingdoms even after the conversion process started in their realms. Rædwald in particular is called out by Bede for his apostasy and maintaining altars to both Christ and his pagan gods. The burial at Sutton Hoo is largely attributed to him and contains both pagan and Christian elements. Animal sacrifices (and human) sitting alongside silver dishes bearing the names of Saul and Paul indicate the uncertain religious affiliations of kings at this time frame.

In the end Christianity won out over the pagan realms and each of the pagan kingdoms fell eventually. The last pagan kingdom was destroyed utterly by the kingdom of Wessex shortly after Bede himself was born.

So what did this process look like on the ground? In many parts of England it seems to have been a relatively peaceful process. According to Bede for example, in some areas the high priests of the old religion willingly converted to Christianity, which is a somewhat suspect claim but, well there it is. He also includes and anecdote about a high priest desecrating his old temple by riding a horse into it and hurling a spear into it and then burning the building. Certain pagan practices were outlawed such as horse sacrifice and consumption, but others, leaving out grain for local spirits and amulet wearing to ward of disease, were allowed to survive. The pagan kingdom of the Isle of Wight was supposedly destroyed and its populace slaughtered, raising this is a possibility in some cases. Pope Gregory the Great was famous for suggesting that the pagan temples should be appropriated into Christian sites, but the actual evidence for this happening in England is to my knowledge non-existent.

Christianity in England has a storied origin, and was connected to the Churches in Francia and Ireland as well as the Papacy. The entire process took roughly a century to be completed and included many relapses into paganism by the Anglo-Saxons. It was not some linear narrative of one mission arriving and evangelizing the entire island in a chain reaction.