Our research concluded that migrants during what’s now thought of as the Anglo-Saxon period were most closely related to the modern Dutch and Danish—and that the modern East English population derived 38 percent of its ancestry from these incomers. The rest of Britain, including today’s Scottish and Welsh, share 30 percent of their DNA with these migrants.That's a quite high percentage as these things go; the people of Turkey are genetically only about 10 percent Turkish. So the new result confirms significant migration into post-Roman Britain.
The data also show mixing of immigrant and native populations within a few decades of arrival.
Equally interesting is the spread of the migrants: according to this data, lowland Scotland and south Wales both have about the same percentage of Anglo-Saxon genes as Sussex or the Midlands. I have encountered several Scots online who hate this, but there is a reason most Scots speak English and already did by the time of Edward I.