A man died at Westminster Tube station, which links directly to the Houses of Parliament, early on Wednesday morning despite efforts to resuscitate him.
MPs later revealed the man was homeless.
It is has been claimed that "many" MPs had previously spoken to the man and assisted him.
Sky News understands someone who works in Labour leader Jeremy Corbyn's office was also in contact with the man and brought him food.
Posting on Twitter, Mr Corbyn wrote: "I've just been told about the death of a rough sleeper right by the entrance to Parliament.
"The powerful can't carry on walking by on the other side while people don't have a home to call their own.
"It's time all MPs took up this moral challenge and properly housed everyone."
Labour MP Neil Coyle, co-chair of the All-Party Parliamentary Group on Ending Homelessness, claimed the death was an "appalling indictment of Government failure".
"When a homeless man dies on the Government's doorstep, ministers must stop ignoring the problem and commit to end rough sleeping," he added.
His party colleague Emma Lewell-Buck revealed that - if the identity of the man was as she thought - then she and "many other MPs have spoken to him and helped him out where we could".
Tory MP Heather Wheeler, the Government's minister for homelessness, said the "dreadful news" of a suspected rough sleeper dying at Westminster Tube station will "push me on to find solutions and to work to eradicate rough sleeping for good".
A spokesperson for the Ministry of Housing, Communities and Local Government said: "No one should ever have to sleep rough.
"That's why this Government is committed to halving rough sleeping by 2022 and eliminating it altogether by 2027."
The Government has pledged to spend more than £1bn until 2020 to tackle homelessness and rough sleeping.
Metropolitan Police said a man was pronounced dead at the scene at 7.33am on Wednesday in the underpass of exit 3 at the station.
A spokesperson added: "At this early stage in the investigation, the death is being treated as unexplained but not suspicious."
A spokesman for the London Ambulance Service said: "We were called at 7.16am today to Westminster Tube station, to reports of a man not breathing.
"We sent a team leader, an advanced paramedic, a cycle responder and two ambulance crews.
"Sadly, despite resuscitation efforts, he died at the scene."
A House of Commons spokesman said: "We are saddened to hear of the death of an individual this morning at Westminster Tube Station and offer our condolences to their friends and family at this difficult time."
