Labour's former culture secretary Ben Bradshaw, who is an ex-BBC journalist, said the corporation should publish any evidence it has that it obtained permission from students.
With students, or some of the students, challenging the BBC's account, the BBC must now publish all of the emails and written evidence that it has to support its conjecture that there was full consent.
We know again from recent experience that when the BBC is in the middle of a controversy like this it needs to act quickly - just tell the truth, get the information out there and then people can make their own minds up.
Mr Bradshaw, who sits on the Commons culture committee, added that programme makers should have gone "even further" than usual to get permission and said he was "amazed" they did not secure written consent.
He told BBC Radio 4's World At One programme: "Central to the BBC's editorial guidelines is the principle of informed consent."
More top news
A newly promoted police officer caused a sensation with local women on Facebook
Ex-London mayor Ken Livingstone says he is sorry for the "disruption" caused by his comments that Adolf Hitler was a supporter of Zionism.
Kickstarter group asks for public donations to fund replacing Tube ads with pictures of cats