Dozens of archaeologists are working around the clock under a huge marquee to exhume the skeletons.
Members of the Christie family, which founded the famous auction house, were interred at the St James burial ground.
The graveyard was only ever meant to hold 16,000 graves, but in the end 60,000 were packed in — men, women and children.
Of those, 15,000 are buried under the existing Euston station and will not be moved.
Famous American boxer Bill Richmond, known as the world's first black sports star, is also buried there, along with members of the Christie family who founded the famous auction house.
Archaeologists do know the St James's burial ground, which was converted into St James's Gardens in the mid 1800s, was divided into four sections, with the wealthy being buried close to a chapel and the poor further back.
Many of the name plates and tombstones have been completely preserved thanks to London's damp clay in which they were buried.
"The preservation is really good and we have got a lot of skeletons that have surviving coffin breast plates, and this is really useful because it can give us a name of an individual, a date that they died," said Mike Henderson, the senior human osteologist on the project..
The HS2 train network will eventually run for 531 kilometres and link London to the East Midlands, Leeds and Manchester — but it has raised concern among communities along the route.
Ms Wass said all is being done to limit the damage and respect the dead.
"We are coming face to face with our ancestors and people who are buried here are dealt with dignity and care and respect," she said.
Australia's Interest?
Captain Matthew Flinders never received the accolades he deserved when he was still alive.
Key points:
- Archaeologists will move the remains of 45,000 people buried in a London cemetery to make way for a high-speed rail project
- Matthew Flinders is buried at the cemetery, but his coffin is yet to be identified
- More than 1,000 archaeologists and specialists are working on excavation works along the train route from London to Birmingham
The great navigator died when he was just 40 years old, the day after the book and atlas of his discoveries from his circumnavigation of Australia — A Voyage to Terra Australis — were published.
A kidney infection contracted at sea killed him.
He was buried in a cemetery near what is now London's Euston railway station, not far from his home.