I'm not an expert on military watches but do have an interest in Dennison's. As far as I can tell, these 6b/539s were the old movements (Longines, Omega, JLC and others) from the alloy/steel cased 6b/159s of WW2. The 6b/159s were notorious for leaking and corrosion and so in the usual way, the MoD had the movements recased in stainless steel rather than buying new watches. Dennison's were contracted to manufacture a watertight stainless steel case and this became known as the Aquatite. Aquatites were produced from around 1952 and were made initially in chromed brass with a stainless steel screwback - Edmund Hilliary used an Aquatite cased Smiths for his conquest of Everest in 1953. The Aquatite range were later produced in 9kt gold and are a lovely heavy screwback case - often with Smiths movements. Later on, Dennison's used a version of the Aquatite for the superb 18kt gold Constellations of the 1960s.
I hope that helps
Cheers