The culture secretary is to hold an urgent meeting on Friday with Samir Shah, the chair of the BBC, after the corporation apologised for “serious flaws” in the making of a documentary about the war in Gaza.

Lisa Nandy said she would be seeking assurances that a review commissioned by the BBC’s director general would be “comprehensive, rigorous and get to the bottom of exactly what has happened”.

The BBC has been engulfed in controversy since it was revealed that the 13-year-old narrator of the documentary, Gaza: How to Survive a Warzone, is the son of the deputy agriculture minister in the Hamas government in Gaza.

On Thursday, the BBC disclosed that a “limited” payment had been made to the boy’s mother by Hoyo Films, the independent production company that made the documentary.

Nandy said in a statement: “The public rightly holds the BBC to the highest standards of reporting and governance which is why I will be having an urgent meeting with the BBC chair later today.

“I want assurances that no stone will be left unturned by the fact-finding review now commissioned by the BBC’s director general. This review must be comprehensive, rigorous and get to the bottom of exactly what has happened in this case.

“It is critical for trust in the BBC that this review happens quickly, and that appropriate action is taken on its findings.”

After the BBC board met on Thursday to discuss the issue, the corporation said an internal review identified “serious flaws” in the making of the programme. “Some of these were made by the production company and some by the BBC; all of them are unacceptable … We apologise for this,” a spokesperson said.

They added: “The processes and execution of this programme fell short of our expectations. Although the programme was made by an independent production company, who were commissioned to deliver a fully compliant documentary, the BBC has ultimate editorial responsibility for this programme as broadcast.”

The BBC had asked Hoyo Films several times in writing about any potential connections Abdullah al-Yazouri, the film’s young narrator, and his family “might have with Hamas”.

Since transmission, Hoyo Films told the BBC that it knew Abdullah’s father was a Hamas minister but had failed to tell the corporation, the spokesperson said. “It was then the BBC’s own failing that we did not uncover that fact and the documentary was aired.”

The BBC was seeking further information about the payment made to the boy’s mother.

In a separate statement, the BBC’s board said mistakes made in producing the documentary were “significant and damaging to the BBC”.

Stuart Andrew, the shadow culture minister, called for a “full independent” inquiry into the making of the documentary, and said police should become involved if any payments had been made to “Hamas or their affiliates”.

Andrew told BBC Radio 4’s Today programme that the “possibility of payments being made to Hamas or their affiliates is deeply troubling. That is why we believe there needs to be a full independent inquiry, so we can have absolute faith that everything is being looked at in the round, and make sure we know the processes that were followed or not followed, and exactly how much money has been potentially given to Hamas or its affiliates.”

If it emerged that “public money has got into the hands of Hamas or the official, that needs and warrants a proper criminal investigation”, he said. Hamas is designated a proscribed terrorist organisation by the UK government.

A former senior executive at the corporation said the BBC had made “basic rookie errors” over the documentary.

Roger Mosey, who was the head of BBC television news until 2013, said mistakes by the corporation were “not an unfortunate accident” but the upshot of “some people not doing their job properly and making sure this programme was fit to be broadcast”.

Speaking on the Today programme, Mosey said: “If you’re going to make a film about the most contentious issue in the world today, and where the BBC has to prove its impartiality, you have to get it right. The fact is that the BBC broadcast it, they took editorial responsibility, and then it has unravelled incredibly quickly.

“I think there are some basic rookie errors made here. It’s not an unfortunate accident. It’s actually that some people were not doing their job properly and making sure this programme was fit to be broadcast.”

Mosey rejected claims there was a “systematic bias against Israel” at the broadcaster. He said: “I don’t think the BBC is biased on the big issues of Israel and the Middle East. I think the BBC tries very hard on the most difficult of stories to get it right, and this so undermines it.”

The BBC said it had no plans to broadcast the documentary again or return it to iPlayer.