Lord Bramall, a former head of the British armed forces and a D-day veteran, has died at the age of 95.

Field Marshal Edwin Noel Westby Bramall, an Old Etonian, served in nearly all major UK military campaigns between the second world war and 1985, when he retired from the military.

The decorated veteran took part in the Normandy landings in June 1944 and was chief of the defence staff from 1982 until 1985. He went on to have a 26-year career in the House of Lords, retiring in 2013.

The later years of his life were dominated by untrue allegations he was involved in a VIP paedophile ring, as one of a number of high-profile people who were falsely accused by Carl Beech.

The Metropolitan police commissioner, Cressida Dick, personally apologised to Bramall for the “great damage” the force’s investigation caused to him and his family.

Beech was given an 18-year prison sentence this year for falsely claiming that he had been sadistically abused by figures from the worlds of politics, the armed forces and security services.

Bramall’s home was raided by up to 20 officers in March 2015 while he had breakfast with his wife, Dorothy, who died in 2015 before he was cleared of any misconduct.

He was questioned by police in connection with the controversial Operation Midland. When it emerged he would face no action in 2016, Boris Johnson, then the London mayor, said: “It is pretty clear that Field Marshal Lord Bramall is owed a full and heartfelt apology.”

Dick said on Tuesday: “I’m very sad indeed to hear of the death of Lord Bramall. I met him recently to apologise personally for the great damage the Metropolitan police investigation into Carl Beech’s false allegations has had on him and his family.”

“I was struck by his selflessness and generosity in the issues he wanted to discuss, focusing on a desire to ensure the lessons from Operation Midland had been learned by the Met. It was very humbling to be in his company and hear first hand his experience.

“He was a great man, a brilliant soldier and leader, and much loved family man. He was a true gentleman and will be hugely missed.

“In his memory, and on behalf of all those affected by the mistakes we made in Operation Midland, we are committed to continuing to embed the learning from both the reports by Sir Richard Henriques and the Independent Office for Police Conduct.”

The former defence secretary Lord Heseltine, whose tenure coincided with when Bramall was head of the armed forces, called him an “outstanding soldier”.

He said: “It was an outstanding privilege of my life to work with him in the Ministry of Defence. His public humiliation following the scandalous allegations was one of the most disgraceful episodes of my political life.”

Bramall served as the president of the historic Marylebone cricket club in 1988 and in 1997 was made an honorary life vice-president of the club, which is based at Lord’s cricket ground.

The former defence minister Tobias Ellwood paid tribute to Bramall on Twitter. He tweeted: “An inspirational leader, fellow Green Jacket and mentor who landed on the Normandy beaches, received an MC in Holland a year later, served in our special forces, commanded the British army and then the entire armed forces.”

Bramall and his wife lived at Bulford Manor in Wiltshire during his time as head of the army. The couple, who married in 1949, had two children.