The mythical Anglo, Saxon, Jute, et al, invasion that never occurred. Most Germanic
people arriving in Britain in pre-Norman times were not “invaders”. They were mercenaries hired by the Roman’s as coast watchers and “lowland” police. The Roman’s despised low, swampy ground confiding it very unhealthy. At this time from the Humber south (East Lindsey) through North Folk and South Folk were low lands considered miasmic by the Romans. Thousands of Anglo-Saxons were hired and imported by Rome. Yes, and later there was undoubtedly additional migration occurring from the original German homelands. The Anglo-Saxon were left to it when the few Romans, but mostly Romano-Celts, upped sticks and went back to Rome (few) or Gaul (most) as the empire started to deflate. The Brits are a true polyglot racially. Scratch a Brit and you get Celt, Roman, Norwegian, Dane, Swede, Anglo, Saxon, Jute, Hollander, Gaullic, Briton, etc. The amazing thing is that these groups did not start to mix genetically ‘til post 1500. Many communities maintained very strong genetic origins well into the twentieth century. The preceeding is just a quick gloss-over. The true origin of the British people is a complex fascinating study.
When I was in grade school, there was a woman who did the blood work at our pediatrician's office who was an immigrant from England. I remember her saying that the English people were "mutts."
The Germanic invasions of the 3rd century (in the Roman Empire, "the crisis of the 3rd century") led to the Roman fortification of towns in Gaul (which had to be retaken or rebuilt) and Britain. There are landlubber scholars who claim it would take almost two weeks for the Germans to row across open sea, and yet the fortifications are basically identical in style and date. So yes, there was a Germanic invasion, and it was continual for over a century of the late Roman Empire.
During that time Germans continued to be integrated into Roman auxiliary units, just as they had been since the time of Augustus (he apparently systemetized, or perhaps even invented, the Roman use of auxiliary units, at the termination of the war with Antony).
Around 406ad there was a large, years-long migration in force from across the Rhine, and the western half of the Roman Empire was teetering on the brink. Constantine III (not the same as the Byz emp by that name) pulled his legions out of Britain to assist in the defense, and to press his claim to be Emperor, and of course, from a logistical standpoint, he didn't want to have a barbarian Gaul between himself and Rome.
After the Empire was gone from Britain for good, the Romano-British population was attacked from all directions, including piratical raids from Ireland, Caledonia (the Picts, there was not yet a Scotland), and indeed the Angles, Saxons, and Jutes, and the latter came in far greater numbers than they ever had before, possibly because they were also seeing their homeland in the area of Jutland (hence the name) and northern Germany overrun by yet other Germanic peoples.
There's a good deal of denial and cultural appropriation in Britain relating to this, seen in stupidity like a Victorian-era memorial to the genocidal loser Boudicca, the King Arthur legend, the "Most Ancient Order of Druids" who may as well join the SCA because of their cosplay every year at Stonehenge.
There's an undercurrent of Celtic DNA among Britons, but there's also perhaps a third (as in my case) of Scandinavian DNA from the Danish and Norwegian invasion and settlement in England, and indeed and probably more thoroughly in Ireland and Scotland and the Isles. During the Reformation on the Continent, Britain received loads of refugees, and they were from all over. Someone in the recent Shakespeare topic brought up Emilia Lanier, allegedly Shakespeare's Dark Lady, who was from the Bassano family, a group of Venetian Jews whose even earlier roots were in Morocco. The Victorian-era painters Dante G. Rossetti and Louis Alma-Tadema were Italian and Dutch, respectively.