The London Ambulance Service said the Labour leader's staff member, thought to be his driver, gave Mr Smith, 55, mouth-to-mouth resuscitation and cardiac massage for more than 10 minutes until emergency crews arrived at his home on the 35th floor.
The battle to save Mr Smith continued for 80 minutes, until 9.15am, when consultants at St Bartholomew's were finally forced to concede that he had died.
Staff at the hospital delayed the announcement of Mr Smith's death for almost one-and-a-half hours at the request of his wife Elizabeth, 54, so that she could inform members of the family.
Donald Dewar, the Opposition spokesman on social security, and his wife, close friends of the Smiths, were among the first to turn up at the accident and emergency unit, which the Labour leader visited only two weeks ago to support the campaign to keep the unit open.
Shocked staff at the hospital, who had met Mr Smith during the visit, maintained that, had the unit been closed, the journey from his home to The London Hospital would have taken much longer.
Mr Smith complained of pains just after 8am and collapsed just after his wife had called the emergency services. Two Labour party staff members, Jo Moore, a press officer, and another official, were waiting at the flat.
Concerned that the ambulance appeared to be taking some time to arrive, Ms Moore went to the porter's lodge at the foot of the building and called Mr Smith's driver who rushed to his boss's aid.
With no sign of the ambulance, a panicked Ms Moore dialled 999 and asked: 'Where is the ambulance.' She was told it was on its way but was coming from Shoreditch on the other side of the City, even though Bart's hospital is just a few hundred yards from the flat.
Ambulance staff received the first call at 8.11am and alerted a motorcycle paramedic and dispatched a two-man crew from Shoreditch, east London, who were at the leader's home at 8.16am and 8.17am respectively.
Dave Richards, the ambulance service's senior duty officer at Hackney, said Mr Smith was not breathing, had no pulse and was unconscious, but was receiving aid from the member of his staff when the motorcycle paramedic got there.
The paramedic began mechanical ventilation and connected Mr Smith to a heart monitor which showed ineffective heart rhythm. A defibrulator was used to administer electric shocks in an effort to re-establish a regular heartbeat, and adrenalin and atropine were given intravenously.
However, at 8.36am the decision was taken to move Mr Smith on the three-minute journey to Bart's accident and emergency unit, where medical staff had been alerted by a 'blue call', indicating a serious emergency on its way.
Hospital staff continued the efforts at cardio-pulmonary resuscitation, but Mr Smith never regained consciousness and they were forced to concede that he was dead just over 30 minutes later.
Mike Besser, the hospital's professor of medicine, delivered the news in a solemn press conference in the Great Hall.