It was taken to RSPCA West Hatch Animal Centre in Somerset for rehabilitation and will eventually be released back into the wild.
A BDMLR spokesperson said: “After storms and high tides, seals often haul out to rest, digest and recover.
“For very young pups, rough seas can also separate mother and pup or displace pups from sheltered pupping areas.
“In many cases, the mother is still nearby and will return to feed when undisturbed.
“If there are disturbance issues, the mother may abandon the pup altogether.”
The charity said its approach was to reduce disturbance and monitor pups until they were united with their mothers.
But it said if they were unwell or repeatedly approached by people and dogs and there was no sign of their mother, they may rescue the pup for veterinary care and rehabilitation.