My grandfather was Charles James John Law and yes he worked his way up from a PC to Inspector. HIs cousin Percy George Law was also an Inspector at the Yard at the same time and he worked in the photographic section. Charles was in administration.
Charles police and sporting medals were advertised on Ebay but alas I was not the winner of this auction. I found reference to Percy in a 1950 newspaper with an image of him photographing a gun for fingerprints but I would love to know more. Charles grandfather was also an Inspector and I believe some of the other Laws were also in the police force.