Yesterday police officer Simon Harwood was cleared of killing newspaper seller Mr Tomlinson during the G20 protests in London in 2009.
Pc Harwood, 45, shoved the 47-year-old father of nine, from behind and then hit him with his baton, causing him to fall heavily to the ground.
Minutes later, Mr Tomlinson collapsed and died on the street.
Jules Carey, the Tomlinson family's lawyer, said the family had had to fight to see Harwood's disciplinary records by making applications to the High Court.
"When they understood what was in Pc Harwood's records they were really quite shocked and didn't understand why he was in the force," he told BBC Radio 4's Today programme.
"Ultimately, what they would very much like is for the police to accept...Ian Tomlinson's death was unlawfully taken. They would like that to be admitted, they would like a frank apology, but if that doesn't come they will push the issue of liability in the civil court."
The verdict came 14 months after an inquest jury ruled that Mr Tomlinson was unlawfully killed, prompting the Crown Prosecution Service, which had initially declined to prosecute, to reverse its decision.
Paul King, Mr Tomlinson's step son, broke down as he spoke on behalf of the family outside the court and disclosed that they would continue their fight for justice.
"We are not giving up on justice for Ian," he said. "There has to be one more final and formal answer as to who killed Ian Tomlinson and that we will pursue in a civil court."
Pc Harwood admitted he was wrong to hit Mr Tomlinson during the protests in April 2009 but listed a series of more extreme measures he could have resorted to control the situation - including using his gun.
He said: "At the time I believed he was obstructing the police line and needed to be encouraged to move away.
"We don't get time to sometimes think of your options because it is an instant reaction."
It can now be revealed that Harwood's attack on the homeless alcoholic marks the lowpoint of a police career blighted by violent outbursts.
Harwood was due to face internal proceedings in 2001 after being accused of unlawful arrest, abuse of authority and discreditable conduct but these were discontinued when he retired on medical grounds.
He was accused of shouting at another driver and knocking him over his car door, then announcing he was a police officer and arresting the motorist on a common assault charge.
After retiring as a police officer from the Met, Harwood rejoined the force as a civilian worker, then became a police officer for Surrey. He was later allowed to rejoin the Met in 2004 as part of its Territorial Support Group (TSG), specialising in public order.
Ten allegations had been made against the officer during his career before his encounter with Mr Tomlinson, who later died.
In 2005 Harwood was hauled up by his bosses after he was seen to knee a suspect in the kidneys as he lay on the ground.
Again in 2008 he was at the centre of allegations of 'heavy handed' policing after he twisted the handcuffs of a manacled motorist he had pulled over for an apparent speeding offence.
Jurors did not hear evidence of the two incidents after Mr Justice Fulford ruled it would complicate the hearing and compromise its fairness.
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Deborah Glass, deputy chair of the Independent Police Complaints Commission (IPCC), said: "The circumstances of Pc Harwood's return to the MPS (Metropolitan Police Service) in 2004 raised grave concerns about MPS vetting procedures.
"I have commented in previous cases on the damage to public confidence that can result when police officers are allowed to go before disciplinary matters have been concluded - it is all the more alarming when police officers who have avoided disciplinary proceedings by resigning or retiring are able to come back.
"We recommended that the MPS tighten their procedures in this area."
The IPCC will now look again at the evidence given by other officers at the scene when Harwood pushed and hit Ian Tomlinson, and their actions, she said.