The situation wasn’t the same. The Roman colonized a bit of England, but most romanized the local population, leaving the local celtic tribes to the East and North.
The Anglo-Saxon were a bunch of tribes that packed their shit and just decided to live in England. They eventually were more Anglo-Saxon than Romanized Celt or descendent of Roman.
The Norman didn’t migrate to England like the Anglo-Saxon did, it was just a bunch of nobles and soldier. During most of England history after the Norman Invasion, the nobility was mostly french, while the local population (which was a way larger amount of people) were anglo-saxon. Overtime English become more and more used by the nobility and by 1362 by law the court was to be English. The Anglo-Saxon kind of did what the Chinese did to any invaded, have enough people speaking the local population that foreign leader just become assimilated into the local culture.
That said a lot of french root say in English language. Usually you see the difference between the French nobility and the English population. For example, most people would say they eat the animal since they would slaughter it themselves, so they eat pig or cow. But the french nobility was eating meat prepared by other so pork or beef. The word for the animal have anglo-saxon root, while the words for meat have french root.
Anglo-Saxon culture was never really replaced. While the ruling class in England was made up of French-speaking Normans for a long time, regular people were still ethnically Saxon and spoke early English. Modern English has a lot of French (and Latin) in it, but the grammar and core vocabulary is Anglo-Saxon. English legal foundations, like using common law instead of a roman civil law, come from its Anglo-Saxon roots more than its Norman conquerors too.
The Romans settled in England, but most of them returned to the Roman empire when the Roman army withdrew, then the tribes of Angles and Saxons invaded and settled through England, killing or driving all the inhabitants into Wales and other extremes of the UK. When the Normans invaded and conquered the Saxons they didn’t wipe out the Saxons except for the area around York. The Normans just adopted the role of Barons and administrators and governed the Saxons.
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