Well this is why it's more of a smear vs distinct division problem. There were different languages yes, but there was also Common-Brittonic, and later Old English.

So yes you can divide these up into smear groups but also they were mixed significantly enough to also maintain a single shared cultural language across Britain.

If language and cultural history are the definition of ethnicity then these peoples are simultaneously two ethnicities, British and their own sub-groups of gaelic/brittonic/and further subdivisions depending on which point in the history of the island you want to look at and dig into. Like I said to the other user, the clearest and least blurred ethnic distinction historically is probably the anglo-saxon settlers at the specific time of their settling.