A supporting bracket assembly for a horizontal lifeline cable (4) comprises a base plate (14), bracket means (24) and holding means (28) for the cable. The base plate (14) is provided for securing to a structure (6). The bracket means (24) is secured to the base plate and adapted for frictionally restrained pivotability with respect to the base plate and the holding means (28) for the cable (4) is secured to the bracket means (24). In this way, dynamic loading of the cable (4) results in pivoting of the bracket means (24), against frictional restraint, from a first position (36) into a second position (38).