They allege that the force issued "misinformation" about the level of contact until a newspaper published a video six days later showing an officer pushing Mr Tomlinson to the ground and hitting him with his baton.
Scotland Yard's first statement about 47-year-old Mr Tomlinson's death was issued late on April 1.
It said officers tried to revive him after being alerted to his collapse by a member of the public, and suggested that some of the protesters hampered their efforts.
The statement read: "A member of the public went to a police officer on a cordon in Birchin Lane, junction with Cornhill, to say that there was a man who had collapsed round the corner.
"That officer sent two police medics through the cordon line and into St Michael's Alley where they found a man who had stopped breathing."
It went on: "The officers took the decision to move him as, during this time, a number of missiles - believed to be bottles - were being thrown at them."
But on April 7 the Guardian newspaper released a video shot by a fund manager from New York which showed Mr Tomlinson being shoved to the ground from behind by a helmeted police officer.
When the footage was slowed down, the officer could be seen apparently using his baton to hit the newspaper vendor on the leg.
The Independent Police Complaints Commission (IPCC) said its inquiry would be independent and look at how both the Met and City of London Police handled the media.
It will be separate from the IPCC's ongoing investigation into the circumstances of Mr Tomlinson's death.
IPCC deputy chairman Deborah Glass said: "Not only the Tomlinson family but also many members of the public and MPs have raised with us concerns about whether the police either misinformed the public about the circumstances of Mr Tomlinson's death or failed to correct misinformation about how he died.
"I have therefore decided that, not only will we investigate the family's specific complaint about the content and timing of the Metropolitan Police Service (MPS) media communications on the night of April 1, but that we should also seek to determine, as far as practicable, the state of knowledge that both the MPS and City of London Police had about any police contact with Ian Tomlinson between April 1 2009 and April 7 2009."
The IPCC is also carrying out another three investigations into allegations that officers assaulted members of the public at the G20 protests.
Scotland Yard said in a statement: "The Commissioner has made it clear on a number of occasions that Ian Tomlinson's family deserve, and should expect, answers to their questions in relation to his death.
"It is important that there is a transparent process, which provides clarity as to what the MPS, City of London Police and the IPCC said and knew regarding the circumstances of Ian Tomlinson's death.
"Therefore we welcome the IPCC investigation and will continue to cooperate fully with them."