Mr Bradshaw met TV presenter Mariella Frostrup and members of the Shark Trust, to receive a petition signed by 83,000 people opposed to shark finning.
The value of fins is much higher than the rest of a shark's carcase, which is why fishermen are tempted to remove the fin and discard the carcase.
Mr Bradshaw said he was disappointed that UK was not able to persuade enough EU Member States to agree to stronger controls on the finning of sharks. The Shark Trust has been campaigning with the UK for stricter rules.
Mr Bradshaw said:
"I cannot imagine a more barbaric practice than cutting fins
from a shark and then abandoning it to die. The UK has
been pressing with some like-minded Member States for
safeguards to ensure this practice is brought to an end.
Recent Community legislation to restrict the practice of
finning is a step in the right direction but goes nowhere
near as far as the UK would have wanted.