Long-finned pilot whales typically favour cooler, temperate waters beyond the continental shelf in the Atlantic Ocean.
The pod was first spotted on Thursday, but the BDMLR said one showed signs of illness and became separated from the group on Friday morning before being found near East Tilbury.
Kent Fire and Rescue Service, HM Coastguard and Port of London Authority teams attended, along with members of the BDMLR. They found two whales — one deceased and one alive.
The live animal refloated on the incoming tide after dark and rejoined the rest of the group, the BDMLR said.
“The deceased whale was a female measuring approximately three metres, which is around the length for maturity and it is possible that a debilitated member of the pod is the reason for the animals to have come into this unusual situation,” the group said.