Royal Enfield's factory number 4 was located in Feckenham, about 6 miles from Redditch, in the location of a former needle factory overlooking the village green. According to various reports it continued as a private residence. Here is a picture from the 1950's,
Could it be this gray roofed house facing the village green today? Note the angled middle roof and the chimney in the neighboring house,
Google offers a different perspective that even outlines the white sign on the neighboring house next to the chimney in the 1950's picture, is still there!