Before I tell how England was converted, I will first tell who was there to be converted. After Rome withdrew its armies from Great Britain to help defend against the barbarians, another group invaded the island. This group was the Saxons. The Saxons Britain in the four different directions. After they conquered each place, it got a name. The north was called Norfolk, the east was called Essex, the south was called Suffolk, and the west was called Wessex. The original Britons settled Wales.
It was after this that the Gospel came to England. The current king there was Ethelburt, and he was the first to be converted. Where did the missionary come from? His name was Augustine (no, not the latin father) and he was sent by Gregory VII in Rome. After Ethelburt was converted, all the other main court officials followed suit, and when the ruler and other high people change religion, at least then, that is what happens for the whole kingdom.
Previously there had been temples to pagan gods, and many of these were transformed into Christian churches. Three major churches were made this way. Westminster abby was built in the place of a temple to Apollo, St. Paul's Cathedral from Diana's temple, and the cathedral and Canterbery was built in the place of a temple near the kings palace.
Now that England had been converted, more work could be done with the church in general, and England started to become what it is today.