It was the grandsons and great grandsons of Beli Mawr that had to dance to the Roman music as they took control of the island. A detailed chronology of this dance is given by Salway who states that the conquest of the south and east of the island was accomplished by 47 AD. There was a Roman military campain on the Welsh border 47-52 AD. He records the foundation of London around 50 AD, which would of course mean that the Romans had taken Lud's Town before this date. The conquest of Wales was continued 52 AD - 58 AD and reached the island of Anglesey 60 AD. The conquest of northern Britain and Wales was completed 71 AD - 84 AD. So there you have it. The family of Beli Mawr is lost to the Roman world for the next 400 years. Somehow, at least one son Afflech had a lineage to survive. As given by Dwnn:
"Vortiger ap Rhydern ap Dehenfraint ap Eidigant ap Eudeirn ap Enid ap Endos ap Enddolau ap Afallach ap Afflech ap Beli mawr."
This lineage is given in Dwnn, L. Heraldic Visitations of Wales and part of the Marches, Longman & Co., London, 1846. Vol I, pp. xv - xvi.
The chronology is documented in Salway, P. The Oxford Illustrated History of Roman Britain. Oxford University Press, 1993. pp. 539-540.