This may be of some assistance from kellys (dates are dates of publication )
The firm is not mentioned in the 1884 Kellys, but:
1888, 1890
Bruce, Joseph Benjamin, Brassfounders, Exeter passage, Ernest St
1892
Bruce Joseph Benjamin, brass founder, Havelock works, Ernest street, & shop front fitter, 89 & 91 Newhall street
1895 -1904
Bruce, Joseph Benjamin, Shopfitter & Brassfounders, Havelock Works, Exeter passage & Ernest St
1908
Bruce J. B. shop fitters' brass founder, Holloway head & electric light fittings manufacturer, Havelock -works, Ernest street
1912, 1913, 1921
Bruce J. B. Ltd.shop fitters' brass founders, Havelock works, Holloway head.
1932,1933
Bruce J. B. Ltd. shop fittings, general brass founders & stampers & piercers, Havelock works, Holloway head.
1940
Bruce J. B. Ltd. brass founders, Havelock works, Holloway head
1943, 1944
Bruce J. B. Ltd. shop window fittings mfrs. Havelock works, Holloway head
1949, 1950,1956
Bruce J. B. Ltd. shop window fittings mfrs. Havelock works, 15 to 29 Holloway head
1964
Bruce J. B. Ltd. shop window fittings mfrs. Havelock works, Seeleys rd. Greet 11
1973
Bruce J. B, display mfrs, 'Seeleys rd B11.9LN
Kellys end there, so have no further information.
Attached is a map circa 1910 showing where the works are when it is in holloway head, and also approximately the position in Ernest st, When in holloway head I think the factory was where the white space is on the north side of the road, to the right of the map. (I have placed a red cross to mark it) the building to the right of it is either no 15 or 17, and J.B bruce is unnumbered, but between nos 13 & 31. While at Ernest st/exeter passage (marked in blue), I would guess it was the buildings just above the white space between the two.
mike