Are you referring to the Anglo-Saxons (historically ruled by Norman French--themselves descended from Scandinavia) who drove indigenous Britons into Wales, who could have been the descendants of mainland Celts who drove out the theorized Iberian settlers of the British Isles?
One group displacing another has happened multiple times during history.
With assimilation, the immigrants can become the indigenous people.
From the above, the Norman French spoke their dialect of French and were Frenchmen, even though their ancestry traced to Scandinavia.
In this case, and the parallel one in the United States, people are getting a bit jumpy considering those of European descent (or 'aboriginal' British--what's that?) are still set to be the easy plurality. In the British case, Birmingham is just one city, and not even the largest.