Thanks for editing OpenStreetMap.

If a footpath is already mapped as highway=footway, the default access for bicycles, horses, motor vehicles, etc. is already "no". Adding those tags does no harm, but they are unlikely to have any effect on routing software.

It can sometimes be worth adding bicycle=no if there is a sign explicitly prohibiting cycling. Where a sign is present, you can also add the sign itself by adding a node (point) on the path at the location nearest the sign, tagged with traffic_sign=GB:951 + bicycle=no