A man was spotted putting one in his rucksack earlier this week, while a couple allegedly put one in a box on another occasion.
The RSPCA is reminding people that birds take better care of their young than humans can.
The charity says ducklings don’t usually stray far from their mothers and if someone is concerned about one, they should get in contact.
An RSPCA spokesperson said: “We all want to support wildlife and help animals thrive – but while we hope anyone seen moving or taking ducklings from the Thames was doing so with good intentions, we would strongly advise against taking young birds away from their natural habitat.
“Birds take far better care of their young than humans can, and taking baby birds into captivity unnecessarily can dramatically reduce their chances of long-term survival.
“It could also be an offence under the Wildlife & Countryside Act.
“Baby ducks, geese and swans don’t normally stray far from their parents, so the mother will usually be close to them.
“If the parents don’t return within two hours or are found dead, please follow our online advice about how you can help or contact your local vet.”
