This comes after allegations of sexual misconduct in the charity’s Haiti and Chad programmes and claims that the charity failed to provide the full details of either case to the commission or the government.
But there have been questions as to why the commission did not do more when concerns about the charity’s safeguarding function were raised by Oxfam’s former head of global safeguarding, Helen Evans, in 2015.
The commission has maintained that it did act on Evans’s concerns when they were raised with it, but accepts it had lessons to learn about how it kept Evans informed of how the regulator subsequently acted.
Kate Osamor, the shadow international development secretary, said both the Charity Commission and government departments had serious questions to answer.
"Why did they take no action in response to concerns raised by Helen Evans in June 2015 and August 2015?" said Osamor. "Are there other whistleblowers that have brought safeguarding concerns to the Charity Commission only to be ignored?
"It is crucial that we now understand how far this appalling scandal reaches and whether the Charity Commission is operating effectively as an independent regulator."
Bubb told Third Sector that the commission had previously focused too much of its energies on issues such as Muslim charities rather than safeguarding.
"I think generally the commission has been caught on the hop on safeguarding, and it’s clear it has not given safeguarding the sort of priority it should have had," he said.
"The point I made to William Shawcross, chair of the Charity Commission, was there was a lot of concern in the sector about the overemphasis on Muslim charities. The commission put a lot of resources into that, and I said at the time that was disproportionate, but I also said that safeguarding was as important an issue but it was not giving that priority.
"I always felt that safeguarding was a potential time bomb."
Bubb added that the regulator needed increased funding from central government to "beef up its work on safeguarding" and to hire more people with expertise in this area.
Bubb also criticised the regulator’s response to Oxfam, which he said was "pretty shocking" for not demanding more details from Oxfam in 2011 when the charity said it was investigating its Haiti programme, including the charity’s final report on the matter.
"It's not a postbox – it's a regulator," Bubb said. "It should have asked and demanded that report. Apparently, it didn’t."
Speaking on Channel 4 News, David Holdsworth, deputy chief executive of the Charity Commission, said the regulator took robust action on safeguarding and it was a priority for the organisation.
"We updated our safeguarding strategy last year, and we published that," Holdsworth said. "As recently as two months ago it went out and demanded as part of a regulatory release that charities come forward and report to us any incidents they hadn’t. Our use of powers in itself shows that we do take the matter seriously."