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.
– Ben Bradshaw
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."
The decision to go ahead with the controversial BBC documentary about North Korea went "right to the top", the corporation's head of news programming said.
Ceri Thomas denied that the briefing of the students had been "shambolic" and rejected claims that students had been forced to run unacceptable risks during undercover filming of the investigation.
He said: "We think the risks as we explained them to the students were justified.
"But I need to be absolutely clear that if we had any suggestion that lives were at risk or anything approaching that - either the BBC team's lives or the lives of the students - then we wouldn't have gone anywhere near this."
Asked whether the then-acting director general Tim Davie had signed off on the plans, Mr Thomas replied: "I can't be sure that Tim Davie did. I know that Tony Hall (the current director general) has been involved in recent days."
The chief executive of Universities UK, Nicola Dandridge, said they are "concerned about the methods used" in the making of the BBC Panorama programme, after an academic trip with LSE students was used to gain entry to North Korea.
Ms Dandridge said universities must be able to work with integrity and operate in sensitive areas of the world.
"The UK's academics have a global reputation, and it is vitally important that they can be trusted and seen to be working in an open and transparent manner", she said.
"The way that this BBC investigation was conducted might not only have put students' safety at risk, but may also have damaged our universities' reputations overseas", Ms Dandridge continued.
"We regret the BBC's approach in this matter. Universities UK will be seeking to discuss this with the BBC to ensure they fully understand the concerns of the university sector".
Panorama reporter John Sweeney has defended his actions after using an academic trip with LSE students to gain entry to North Korea.
Sweeney told the BBC:
All of the students were at the risk, with respect this was not Torremolinos where they were visiting. They were all aware of where they were going and that a journalist was going.
We told a lie to the agency.
– John Sweeney, panorama reporter
When asked why the students had only been told of a single reporter going on the trip, when in fact there were three, Sweeney, his wife and a cameraman he said: "If I was arrested, then the less the students knew the better, the majority of the students are supportive of the documentary."
The BBC has denied claims that it put students from a London university at risk when an undercover journalist accompanied them on a field trip to North Korea.John Sweeney, a reporter for the Panorama programme, is said to have joined the student group from the London School of Economics (LSE).
He joined them on a visit to the communist country to carry out secret filming.
The LSE says the students "were not given enough information to enable informed consent", and were "endangered", the BBC reported.
The LSE's director, Professor Craig Calhoun, accused the corporation of "lies and deception from the outset".
He told Sky News the BBC was "unwilling to take responsibility" for the risks it caused to students.
The BBC denied giving students insufficient information about plans for secret reporting.