If you study Kubrick you will find he had an obsessive eye for whatever interested him. He wasn't British (an American by birth) though he did move there after "Spartacus" because he was disgusted with Hollywood. Regardless, to answer your question, Kubrick was about exploring the loss of human qualities through extreme situations.
His focus was on being a filmmaker. He cast people because they fit his vision of a film. He shot in locations that matched his vision. If it wasn't they way he wanted it, he would build it. He was incredibly focused and wouldn't finish a film until it was perfect in his eyes. This dedication (madness) resulted in only 12 feature length films in a period of 40 years. If you think about his contemporaries, Scorsese (40+), Bertolucci (20), Polanski (30+), this is a really small output.
Kubrick was known to spend hours on a single shot and to be a maddening perfectionist. Some considered him a huge pain in the ass. I read about the challenges on the set of "Barry Lyndon" when he insisted on shooting by candlelight to ensure the authenticity of the film. As you are aware, candles go out, melt and can be very temperamental. A special, very expensive camera and film had to be used to make it work. It made people nuts.
He did do a film on the French Military early in his career called "Paths of Glory." It' has a lot of similar sentiments as "Full Metal Jacket." However, all of his films focus on how his characters lose their humanity when placed in strange, even absurd situations. This dehumanization is what interested him and so, he wouldn't ever even consider tackling a "subject" like the British Military unless the story worked with what he was trying to say with his films.