What was the legacy that the Romans left the Britons?

Roman civilization in Britannia was wrecked by the Anglo-Saxon invaders who were rural people (this means they did not live in urban centers); illiterate in their native Germanic tongues—their culture was orally transmitted—and also totally ignorant of the Latin language. Also, in the eyes of the Christian Britons, they were heathens since they worshipped their own Germanic gods.
All this means that most features of Roman civilization as had been developed in Britannia did not actually survive the Anglos-Saxon invasions. In the first place, since the Anglo-Saxon unit of social organization was the rural village (or township) Roman towns fell into decay and eventually ruin—which means that there are few public buildings left. The rural villages were communities of peasants who had very little in common with the owners of the former rural villas. Second, those Britons who survived the initial struggles of the invasions later also fell prey to famine or disease, were sold into slavery, fled to Wales or Caledonia or mingled with the Anglo-Saxons. This means that the Latin language and Christian religion did not survive in former Britannia. Nor could dioceses have survived since they are areas under the authority of a bishop and we have just said that Christianity did not survive the Anglo-Saxon invasions.
What was the actual Roman legacy? (See PP presentation) It consists of Roman roads and Celtic Christianity. This is so because those Britons who fled across the mountains to Wales, Scotland and across the sea to Ireland preserved their Christian religion. However, since they held the Anglo-Saxons in contempt, they made very few efforts to convert them to Christianity until the late 6th century.
How were the Anglo-Saxons converted to Christianity? By a Roman—i.e. from the Pope’s see in Rome—stream/mission that arrived in the south of England in the late 6th century and also almost simultaneously by a Celtic/Irish stream that preached in the north. The Anglo-Saxons received their church organization into archbishoprics, dioceses and parishes from the Roman stream. The Latin language—which was the means of scholarly communication and learning from the times of the Roman empire until the 16th century—was also reintroduced by the Roman mission at this time (See also PP presentation).
Finally, as to the features of the English language, it derives its syntax and part of its vocabulary from the Germanic languages of the Anglo-Saxons and another large part of its vocabulary from the Latin of the Church and the French introduced by the Normans. If you reread Gillingham you will understand now why a cultivated Englishman after the conquest was trilingual.