Gallic appearance

[Artorius1960]

IMO the problem with your argument is numbers, there are other factors more important than numbers.

Numbers are only a part of it. I think the of the Frankish overrun of Gaul, the Visigothic overrun of Spain--like the rapidity of the Norman conquest--have a lot to do with the pre-existing culture remaining intact.

The Arabian conquest in the VII and VIII centuries changed culturally North Africa and Spain, however the Arabs themselves were very few.

The Arab conquests were also rapid, but Islamic culture is more all-embracing than the other conquering cultures. The Muslim Arabs were not content with merely having governmental power over their conquests, they wanted to transform the societies they conquered. The spread of Islam by coercion was the reason for the conquests.

IMO should the Britons have had a firm romano/christian culture they would have absorbed the Saxon invaders as it happened with other Germanic invaders in Gallia, Italy or Spain.

I think that the Romano-British culture in Britain was firm. It managed to resist the Anglo-Saxons for several generations--unlike the cultures in these other places. The length of the conflict ultimately ended with the destruction of the Romano-British culture in large sections of Britain. The culture only survived in the fringes of the island.