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Diana, in fact well done! We of England do in fact descend from the Britons and the Anglo-Saxons, and of-course with some contribution from Romans and Normans, and some individual groups that emigrated over the centuries to join up.
The reason why we also descend from the Britons is that the Anglo-Saxons couldn't learn, no matter how they might have tried, Celtic, which the Britons spoke. So, those Britons who didn't move to Wales, southern Scotland, Cornwall, Ireland and Britany, but remained, eventually, within a number of generations, learnt to speak Anglo-Saxon, or olde English.
This is no myth! The Franks, a part of the Visigoths and the Burgunds who moved to Gaul in the fifth century, (and later the Normans in Normandy) although controlling the military and running their respective States, all, within generations, started speaking neo-latin French, which is what the local Gauls spoke (who had given up Celtic for Latin during the Roman Empire), meaning that the Gauls had remained the majority of the population in what later became France. Likewise, the Longobards in northern, and to an extent central, Italy, although being in command of the State which they governed, all eventually spoke Italian and became Italians, as the Italic (Italian) population speaking neo-latin Italian had remained the majority. Likewise the Visigoths in Spain eventually spoke neo-latin Spanish, as the Spaniards had remained the majority.
Again, the Vandals in North Africa blended their culture with the Carthagians, and didn't expel them.
So, as the Britons had never given up Celtic for Latin, when the Anglo-Saxons came, there was no reason why they should have sent every Briton away, many of whom did remain, only, they couldn't adapt to the Celtic language, so the Britons remaining adapted to the Anglo-Saxon!