About 2,000 items are thought to have been stolen from the British Museum, but some of the missing treasures have started to be recovered, chairman George Osborne has confirmed.
The ex-chancellor told BBC Radio 4's Today programme "more could have been done" to address the thefts sooner.
A member of museum staff suspected of involvement has been sacked.
And Hartwig Fischer, the museum director, will step down after saying a 2021 investigation was mishandled.
The museum, one of the UK's most prestigious cultural institutions, has been under pressure since revealing earlier this month that a number of treasures were reported "missing, stolen or damaged".
The items involved dated from the 15th Century BC to the 19th Century AD and had been kept primarily for academic and research purposes, the museum previously said.
Mr Osborne - who was appointed as chair of the museum in June 2021 - told Today "we have already started to recover some of the stolen items".
"We believe we have been the victim of thefts over a long period of time and frankly more could have been done to prevent them," he said.
Asked where the missing items were located, he said "some members of the antiquarian community are actively cooperating with us" and that recoveries so far were a "silver lining to a dark cloud".
He said he was confident that "honest people" will return items found to have been stolen, but acknowledged that "others may not".
The museum is working closely with the police, Mr Osborne said, adding that a "forensic job" is under way to establish precisely what is missing. He said security at the museum needed to be improved.
Asked why concerns raised in 2021 were not taken seriously, Mr Osborne said it was "possible" that "groupthink" among senior museum staff meant they "could not believe that there was an insider" stealing treasures.
He acknowledged that the incident has damaged the museum's reputation but said he was focused on "cleaning up the mess".
A man has been interviewed by Metropolitan Police detectives over the missing items but no arrests have been made.
Senior figures at the museum have scrambled to address how they handled the discovery of missing items after it emerged concerns about potential thefts were first raised two years ago.
Mr Fischer, who has held the position of director since 2016, confirmed on Friday that he would leave his role once an interim replacement had been appointed.
He was previously due to step down in 2024.
In a statement, he said: "It is evident that the British Museum did not respond as comprehensively as it should have in response to the warnings in 2021, and to the problem that has now fully emerged.
"The responsibility for that failure must ultimately rest with the director."
Tim Loughton MP, the Conservative chairman of the all party parliamentary group for the museums, has rejected claims it is no longer a trusted custodian of its vast collection, which numbers more than 80 million items.
He said calls for artefacts to be returned to their countries of origin were "opportunistic", telling BBC News culture and media editor Katie Razzall other countries should be "rallying around to help retrieve objects instead of trying to take advantage".
Mr Osborne said the British Museum plays a vital role in bringing together important collections from around the world, adding: "In an age that we are always reminded what divides us, it is a place that reminds us of what we have in common."