The Seal Research Trust backs calls to make deliberate seal disturbance an offence.
Getting too close to the animals spotted along the River Thames can be harmful for both them and members of the public, a charity says.
Staff monitored the pup for 48 hours to see if its mother would return before rescuing it.
Grey seal pups can be seen on the Isle of Man from late August until mid-November.
An underweight common seal pup which is rare in Guernsey is being cared for at an animal charity.
British Divers Marine Life Rescue believes the male common seal will make a full recovery.
The amount of people ignoring guidance on Norfolk's coastline is "relentless", a charity says.
Scientists monitoring seal pups worry if a hospital is not set up quickly more pups will die.
Scientists say 13,000 southern elephant seal pups on Heard Island have died of the H5N1 strain.
