Here is a paste of the comment made by gweilo8888 that explains his investigation.
OK, this one I am not so sure of -- but I'm 90% sure I have it.Anyway, I'm happy to stick this one up, especially considering that the film was shot in 1986 - not long after the company Gweilo8888 was talking about was first registered. If anyone feel differently then please feel free to add a comment. In the meantime here is a Streetview of Mercury St as it looks today (sadly no longer a street market).
I found a higher-res version of your screenshot, and the English on the sign near the center is "Po Kin Hong".
From the HK Companies Registry, I found the following Chinese company name, registered in 1986, and matching the characters on the sign: "保健行".
A search of Google Books for those characters, plus the characters for Hong Kong, turns up the following in a book: "保健行香港北角水星街 22 號, 5-700073". Translation: "Po Kin Hong No. 22 Mercury Street North Point Hong Kong, 5-700073".
This is where my guess gets a bit flimsy: the book is dated 1984, two years after the company registration. Perhaps the company existed under another name prior to its registration -- it had already changed from "Din Flower Ltd." to "Po Kin Hong Ltd" earlier that year.
What makes me think I may be right, though, is that the address above is on an uphill street adjoining King's Road, and the latter has tram tracks on it -- matching the uphill slope in the screenshot, and your note that a tram passes by in the background.
If this *is* the right address, Po Kin Hong's building has been demolished, and the current building dates to 2001 according to Centamap.
Vincent Mansion, the next building back, dates to 1982 and the small first-floor balcony / fence seem to match, although the fence color has changed.
Further back, Hoi Sun Building again postdates the film, and the remaining two buildings on the block while old enough are too far back to see in the screenshot.
So... that's the theory. I think it's Mercury Street, just above the small dogleg. But I can't definitively prove it.