Therefore, its known narrative elements are not a part of the Doctor Who universe as we, on this Wiki, choose to define it. It may have been the basis for a similar story in another medium, however — and that story may indeed be valid.
The story involved the departure of the Romans from Britain around the start of the fifth century in the midst of clashes against the Celts and the Saxons, culminating with the time travellers fleeing the indigenous savages back to the safety of the TARDIS.
The story was first submitted on 2 September 1963. Story editor David Whitaker asked Hulke to revise his original storyline, however; he felt that the plot with its many opposing factions was too complicated, and also that the serial's conclusion echoed that of 100,000 BC too closely. It was hoped that an amended version of Britain 408 AD might occupy the sixth slot of Season 1 (Serial F), to be directed by Christopher Barry, but on 23 September it was decided that the production block did not need another historical story and Hulke's serial was abandoned. The spot in the schedule was ultimately occupied by The Aztecs, while Hulke began work on The Hidden Planet instead - which also ultimately went unproduced.
Following Whitaker's departure, Hulke resubmitted Britain 408 AD (presumably with Susan replaced by Vicki). It was rejected on 2 April 1965, by Whitaker's successor, Dennis Spooner, because the Romans had already featured in his own The Romans. (REF: Doctor Who The Handbook: The First Doctor, DWMSE 7)