The museum, one of the most visited in the world, has been dealing with the aftermath of the thefts, which highlighted internal failings and led to the exit of its director.
"Essentially we were the victims of an inside job by someone we believe, who over a long period of time was stealing from the museum and who the museum had put trust in," its Chair George Osborne told parliament's Culture, Media and Sport committee.
"There are lots of lessons to be learned," he added.
Osborne estimated that about 350 artefacts were in the process of being returned.
The museum, which holds treasures such as the Rosetta Stone and the Parthenon marbles, sacked a member of staff over the thefts, which are also being investigated by London's Metropolitan Police.
It has also said the stolen items included gold rings, earrings and other pieces of jewellery dating back to ancient Greek and Roman periods, as well as small objects such as gems that were often set in rings.
"We have taken steps to improve security and are now confident that a theft of this kind can never happen again," the museum's interim director, Mark Jones, said in a statement.
"But we cannot and must not assume that the security of the collection, in a wider sense, can be achieved simply by locking everything away. It is my belief that the single most important response to the thefts is to increase access."
The proposed digitisation project would take five years, with 2.4 million records to upload or upgrade. Its collection totals at least 8 million objects according to the museum's website.
The museum, which has resisted calls from many countries, including Greece, to repatriate historical treasures over the years, launched a public hotline last month appealing for help in locating the stolen items.
