Certainly not there now, Ludgate Hill is on the borders of the financial district, not part of the jewellery district around Hatton Garden or the old gunmakers in and around St James's.
Just a totally useless aside but an fun story. Hiram Maxim was based in a house in Hatton Garden, then a close knit collection of residential houses now in multiple occupancy as jewellery businesses.
He used to test his prototypes of the machine gun bearing his name in the back yard. Can you imagine that today?