"Flowers of the Forest" is mainly Scottish. It's not originally military, and it's a beautiful tune if you can find a NON-military version (sung, flute or fiddle). The pipe version is a horrendous mutilation.

"Abide with Me" or "You'll Never Walk Alone" are more neutrally pan-British. If you want to reference the 1950s and 1960s specifically (which I guess is when most of the deaths took place?), "Abide with Me" is probably your only option. Or perhaps "Blow the Wind Southerly", which everybody in Britain at that time would have known, and has the right feel, but it isn't and wasn't commonly used for memorials.