Frontline firefighters in Manchester who turned up two hours late to the Manchester Arena bomb last year have nothing to apologise for, according to Andy Burnham, the mayor of Greater Manchester.

Some firefighters asked for forgiveness after an independent review into the arena terror attack criticised the fire service for playing “no meaningful role” in the aftermath of the bombing on 22 May last year.

Poor communication and a risk-averse culture led to fire chiefs preventing the service from deploying until two hours after the bomb went off, according to a review by the former civil service head Bob Kerslake this week.

But Burnham published an open letter to firefighters on Friday in which he said: “No frontline firefighter has to apologise for anything. You and your colleagues did nothing wrong that night.”

Quick Guide Manchester Arena bombing report: the key points Show • The Greater Manchester fire and rescue service did not arrive at the scene and therefore played “no meaningful role” in the response to the attack for nearly two hours. • A “catastrophic failure” by Vodafone seriously hampered the set-up of a casualty bureau to collate information on the missing and injured, causing significant distress to families as they searched for loved ones and overwhelming call handlers at Greater Manchester police. • Complaints about the media include photographers who took pictures of bereaved relatives through a window as the death of their loved ones was being confirmed, and a reporter who passed biscuit tin up to a hospital ward containing a note offering £2,000 for information about the injured. • A shortage of stretchers and first aid kits led to casualties being carried out of the Arena on advertising boards and railings. • Armed police patrolling the building dropped off their own first aid kits as they secured the area. • Children affected by the attack had to wait eight months for mental health support. Photograph: Oli Scarff/AFP

He said he knew that many were desperate to help that night, “but were prevented from doing so by decisions taken above you. The failure is not yours but one of process, leadership and culture.”

One unnamed firefighter told the Manchester Evening News he wanted to ask for forgiveness from those affected by the attack. He said he had been ordered by his bosses to move three miles away from the arena after the bomb exploded, leaving paramedics to use his base at Manchester Central fire station, which is just 0.6 miles away from the concert venue.

The firefighter described how he and many of his colleagues have found it impossible to come to terms with what happened.

He said: “I would like to ask for the forgiveness of the victims, their families, and other emergency service workers for not upholding my end on the night.

“If it ever happens again I will do what I should have done on that night – pick up the first-aid bag off the taxpayers’ fire engine and walk to the incident myself, or hitch a ride with the true heroes of the incident — the ambulance service.

“Many of us have been left distressed and devastated by what happened.”

Burnham commissioned the review by Lord Kerslake after firefighters contacted him in the days after the attack expressing their frustration at being prevented from helping that night.

He told the whistleblowers: “Let me be clear: you were right to speak out and you should be proud that you did.”

The chief fire officer in charge during the arena attack took early retirement in September. His successor, Dawn Docx, said Greater Manchester fire and rescue service was cooperating fully with a wide-ranging review into its culture and practices being carried out by the deputy mayor, Beverley Hughes.