As a sub-lieutenant on HMS Bulldog in 1941, Mr Balme led a boarding party on to the captured German submarine U-110.
Inside he retrieved an Enigma cipher machine and documents which contained secret settings and procedures for the sending of coded military messages.
It was the first of only three U-boats ever to be boarded by Allied servicemen during the war, and the episode provides the basis for a major new American movie, U-571.
But the film, which is released in the UK on Friday, has sailed into a storm of controversy for putting a very American spin on events.
Thanks to some creative scriptwriting, it is the Americans, not the British, who stage the daring Atlantic assault.
However, Mr Balme is sanguine in the face of the controversy.
"It brings home the whole Battle of the Atlantic to a generation who otherwise would have known nothing about it," he says.
Balme on board
His eagerness to accept this remarkable reinterpretation of history is, in part, down to his own involvement with the blockbuster.
As word of the project leaked out last year, and anger among British veterans began to stir, Mr Balme was co-opted into the venture by the movie's director Jonathan Mostow.
It meant spending two weeks in the company of the crew during filming off the coast of Malta, in the Mediterranean. The 79-year-old was consulted by Mostow and bonded with the film's star's Matthew McConaughey, Jon Bon Jovi and Harvey Keitel.
"They were a marvellous bunch. Matthew McConaughey is a terribly nice chap. Harvey Keitel has a wonderful manner and is a fantastic actor."
There was even talk at the time of Mr Balme taking a bit part as a coast guard, although this never came off.
Mr Balme admits he was sceptical when he first heard of the project.
"I was a bit surprised and initially I thought it was a pity. But I don't know why anyone complains because no-one had heard of this before the Americans made the film.
"Once I got working with them I realised that the scale they were going for was beyond the budget of a British film."
He failed to convince Mostow to include a message at the beginning of the film making clear it was a work of fiction, but did win one important concession.
Towards the end of the picture, a written dedication appears on screen, honouring the Royal Navy's role in the capture of U-110.
Fear factor
While Mr Balme is glad of the renewed recognition afforded to those who fought in the Battle of the Atlantic, the experience has reawakened the fear he suffered when leading the boarding party on 9 May 1941.
The decision to board the captured vessel was unusual, he says. Normally it would have been rammed or abandoned to sink to the sea-bed. As Sub Lt Balme, then aged 19, climbed on board he knew the sub could either be booby-trapped or Germans could be lying in wait.
Descending the steep ladders that took him down the conning tower required two hands, leaving him totally defenceless.
"Going down those ladders and thinking there may be Germans ready to shoot you ... it was terrifying. We couldn't believe that they would have just abandoned this submarine.
"It was something that haunted me for 15 or 20 years afterwards."
His judgement on Hollywood's interpretation is far more upbeat. Mr Balme has already seen U-571 twice and he thoroughly approves.
"It's a great film. It's all blood and thunder and the young people will love it."