Charles made his comments during a visit to the 3 Royal School of Military Engineering (3RSME) at Gibraltar Barracks, Minley, Surrey.
The King, who is colonel-in-chief of the Royal Engineers, was met by the Lord Lieutenant Nigel Atkinson and Major General Eldon Millar before he received a salute from a Quarter Guard comprising officers from the school.
As he was led into the officers' mess by Lieutenant Colonel Robert Grant, commanding officer of 3RSME, the King said to him: "I do apologise for taking you by surprise, when this opportunity appeared and I had been allowed out of my cage, I wanted to come to have a look."
Lt Col Grant told the PA news agency: "We only had six days to pull this together but the only answer from us was 'yes'.
"There was a palpable sense of excitement as you saw the units spark into life for the visit."
The King then met with groups of engineers and their families where he learnt about their experiences training at the school and the support they receive from their loved ones.
He shared a joke with Natalie Newman, the wife of Corporal Joseph Newman, when she told him that they had three children.
The King has visited the Gibraltar Barracks training base for army engineers in England. (AP PHOTO)
Charles told her: "Nothing a strong drink won't help."
When Cpl Newman told him that his role was as an electrician, he said to his wife: "Terribly helpful to have an electrician around."
She replied jokingly: "Well, you say that!"
"He was really funny, he appeared absolutely fine and upbeat," she said afterwards.
Cpl Newman, 32, said: "He is a really lovely person, he liked to engage with you, it wasn't a fleeting chat, it was an in-depth conversation."
The King also met officers from the 8 Engineer Brigade HQ, which provides engineering support to military operations and, before he left, Charles signed the regiment's visitors' book and was presented with gifts of flowers and Royal Engineer china mugs from the children of some of the barracks' serving soldiers.
He also took the chance to meet families and staff members who waited outside to see him leave and the King told them: "Aren't you all meant to be having lunch?"
The King was then presented with a portrait of himself drawn by six-year-old Louie Bacon, son of Warrant Officer 2 Mark Bacon.
Louie said it was good to meet the King and he was very excited.
Mother Kim Lewis, of Fleet, said: "It was really exciting, a once-in-a-lifetime chance, definitely worth half a day off."
The 3RSME was formed in September 1939 as the Combat Engineer Centre of Excellence.
All Royal Engineer soldiers and officers pass through 3 RSME to receive combat engineer initial trade training.
The school is responsible for providing command courses at the junior and senior level, as well as combat engineer courses, teaching skills such as bridging, demolitions and water supply.
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