The Metropolitan police have issued a formal apology to the family of a newspaper seller killed by one of its officers during the G20 protests in London four years ago, accepting for the first time that “excessive and unlawful” force had been used.

The family of Ian Tomlinson said Scotland Yard’s statement marked the end of a long legal battle in the face of untruthful accounts and obstruction by PC Simon Harwood, who assaulted Tomlinson, and other officers.

“The public admission of unlawful killing by the Metropolitan police is the final verdict, and it is as close as we are going to get to justice,” Tomlinson’s widow, Julia Tomlinson, said.

The family had faced “a really hard uphill battle” to get to the truth of what happened to her husband in April 2009 as he tried to make his way home through the G20 protests in London, she said.

The statement from Deputy Assistant Commissioner Maxine de Brunner of the Met – and an undisclosed financial settlement – marks an embarrassing climbdown by the force.

“I apologise unreservedly for Simon Harwood’s use of excessive and unlawful force, which caused Mr Tomlinson’s death, and for the suffering and distress caused to his family as a result,” said De Brunner.

The police statement apologised for not informing the family that Tomlinson had been assaulted by an officer and for issuing misleading statements in the immediate aftermath of his death, when the force said officers had come under a hail of missiles as they tried to go to his assistance – a version of events repeatedly questioned by witnesses who spoke to the Guardian.

De Brunner said: “The commissioner also apologises to the family for ill-considered comments made in the media in the immediate aftermath of Mr Tomlinson’s death which served to distract attention away from the investigation into the death. Further, it is a matter of deep regret that Mr Tomlinson’s family learned of the nature of his contact with Simon Harwood through the press, rather than from our officers. I fully appreciate and regret the distress.”

Tomlinson collapsed as he tried to find his way through police lines in Cornhill, near the Bank of England, during the protests four years ago. He had been an alcoholic for several years and it was initially presumed he had died from natural causes, a conclusion supported by a first postmortem examination, which gave the cause as heart failure.

But six days later the Guardian published video footage shot by an American in London on business which showed a police officer – later identified as Harwood – in riot gear striking Tomlinson on the leg with a baton before shoving him violently to the pavement, minutes before his final collapse.Monday’s statement admits that at the time of the attack Tomlinson posed no threat and was obeying police instructions.

Three pathologists involved in two further postmortem examinations said Tomlinson had died from internal bleeding associated with his liver and consistent with being pushed to the ground.

The family decided to take civil action against the Met after being left with two seemingly contradictory verdicts. An inquest jury took just three hours to decide that Tomlinson had been unlawfully killed by a police officer. But a jury in a subsequent criminal trial found Harwood not guilty of Tomlinson’s manslaughter.

Speaking on behalf of the family, Julia Tomlinson said: “We have had to deal with many obstacles and setbacks. After the unlawful killing verdict at the inquest it was unimaginable to us that PC Harwood could be acquitted of the criminal charge of manslaughter. We will never understand that verdict … It will always be painful for us that Ian died so violently, but at least he is at rest now, and the force has publicly acknowledged the truth.”

De Brunner went on to apologise for a failure to vet and discipline Harwood properly over a string of previous disciplinary hearings and on behalf of a police officer who wrongly told two pathologists that Tomlinson had fallen to the ground in front of a police van before he came into contact with Harwood.

“It is clear that insufficient recording and checks meant that detailed information regarding the officer’s misconduct history was not shared at key points,” she said. “We got it wrong. The commissioner acknowledges that this case has highlighted significant failings in the vetting procedures of the Metropolitan police service and we have taken steps to put in place new procedures that will improve public confidence.”

However, despite the string of apologies, the Met confirmed on Monday night that no officer – except Harwood, who was sacked for gross misconduct in September last year – had faced disciplinary action.

Julia Tomlinson, on behalf of her family, said the statement marked the end of their four-year fight for justice. “It has been hard to keep going sometimes. We’ve taken strength from the support that we’ve received from so many people who have walked with us and sent us kind messages over the years. It has meant a lot to us. “

Tomlinson also thanked her legal team, the two people who went to Tomlinson’s aid after he collapsed, Christopher la Jaunie, who shot the video footage, and the Guardian journalist Paul Lewis, who broke the story of the video and carried out extensive investigations into the case.

Paul King, one of Tomlinson’s sons, said it was now time for the family to move on and begin to “grieve properly” for his father. “The next step for me and the only other step is to move on and grieve properly for my dad ... The memories of Ian are the video and the last moments of his life, and they’re not very nice memories to have of your dad.”