“The proposed rule 163 states: ‘Cyclists may pass slower-moving traffic on their right or left’.
“It has never been suggested that horses are slower-moving traffic, but the BHS will be asking for the following wording to be put in the Highway Code: ‘Cyclists should NEVER pass horses on the nearside or to their left’. This will avoid any confusion or debate, and this view is supported by British Cycling, British Triathlon and Cycling UK.”
The trouble is that cyclists could interpret that to mean any sort of traffic, horse included, if it is going slower than you. Unless it states categorically you MUST NOT pass horses on the left they will interpret it to suit themselves.