Blackpool itself wasn't really much of a thing yet and post-roman britain can be a little fuzzy in places but here is what we know to the best of my knowledge.

As the Romans evacuated Britain initially the region initially it was native Britons who came to rule the region, we hear of the odd more substantial king who are described as being the leader or king of Britons in general like Vortigern and Ambrosius Aurelianus but whether they actually ruled over all of post roman Britain is hard to verify. Either way this certainly didn't last indefinitely as we see the formation of smaller the northern, native britonnic kingdoms known as Hen Ogledd. Which of this collection of northern hold outs ruled the area that would become blackpool at any given time is hard to say. Possibly Rheged, maybe the vaguely mentioned Regio Dunutinga. The exact borders of any of the kingdoms are unknown today and during their time may have been pretty hazy and changeable to.

Concerning outside conquerors while this region might have experienced some raiding earlier on, perhaps by the Irish or Picts coming down the coast it probably would take a while for it to be conquered by a power forign to the region, probably between 200 and 250 years. The Anglo-Saxon Deira was established on the east coast of modern England, these people would have come from a variety of places along the north sea of continental Europe probably within a life time of the Roman withdraw from Britain. But it took a while for them to push west into the northern Brittonic kingdoms of the region. It was probably not long after Deira conquered the region where Blackpool is today that it would unit with another saxon kingdom of Bernicia to form the more famous kingdom of Northumbria.