The High Commissioner of Australia to the UK, George Brandis, told the Telegraph he hoped a suitable memorial could be created to mark the spot Captain Flinders will be interred.
He said: “The Australian government, the Flinders family, the relevant civic and ecclesiastical authorities will have a discussion about the reburial of those remains and the creation of a permanent memorial to him.
“I’d envisage they would be interred near to the location where they were discovered, with a suitable gravestone.
“I would make the case (Captain Flinders) is one of three great figures of the discovery of Australia by Europeans, along with Cook and Phillip.
“It does well, particularly at a time like this, for English people to be reminded what a central role they played in the development of other nations.”
The find comes fewer than three months into the recovery work at St James’s Gardens, where burials took place between 1788 and 1853.
Other notable figures laid to rest at the site include Bill ‘the Black Terror’ Richmond, a former slave from New York who was reputed to have taught Lord Byron to spar.
It is one of 60 archaeological sites along the HS2 route that are due to explored as part of the multi-billion pound project, a move that has prompted protests by environmental campaigners.
Construction of the HS2 station is due to begin in the area later this year.