If one tried to conjure an image from just the phrase "HMS Flying Fox", this probably isn't what would spring to mind, is it? It's not a ship, it's not flying, and it's not a fox, for starters.

Royal Navy Reserves HQ for Wales & South West of England, I think it says on the sign at the far end.

Note the Egyptian kings on pillars at the top of the pilasters bracing the doorway. No earthly clue what they're doing there. As usual, Bristol's historical sources seem to peter out south of the river.

Wikipedia says on Egyptian Revival Architecture:

By the end of the 19th century, the style had very nearly disappeared, but in 1922 with Howard Carter's discovery of Tutankhamun's tomb the style underwent a dramatic revival it was used particularly for cinema architecture and sometimes for factory buildings.

...and given the surroundings it wouldn't entirely surprise me to find that this was originally a factory, at least, though the 1940 date in between the Egyptians suggests they were a little late with the styling.