Bench marks are points in the real world where the latitude and longitude (and usually the elevation) are recorded to a very, very high accuracy and precision. In the real world, these are marked by small brass discs set in concrete (or bedrock) that include certain information on them. Bench marks are necessary for accurate surveying by providing well-established starting points for measures and triangulation.
The "BM" followed by the height above datum ie. "BM 27.6" are indeed bench marks Derek. Can't check the grid.ref as I don't have a decent scale map OS map of the area, but.... "living rock" ? Could it be on the sandstone rock face near a certain set of tunnels/air raid shelters on Hoylake Road? From memory, that's the only exposed "living rock" around that neck of the woods.
Which is Bidston Village Road near the junction of Boundary Road. If you look along the wall to the right you can see what looks like the benchmark just above the rock where the sandstone wall starts.
Wherever it had B.M on a map would there have been a real life marker (a plate, rivet etc)? I find it more interesting now looking at maps and seeing the heights (above sealevel?) I tend to think of most roads as on the same level unless I see a visible slope eg Main park entrance to the church at top of Oxton Road
