Two possibilities Peter.
1) The battery capacity has reduced to a tiny fraction of original through normal ageing, such that your charging system easly keeps it fully charged but only within the confines of its much reduced capacity. This allows it to show a normal voltage reading when ignition first turned on, but dropping to almost nothing when starter is asked to operate as the current demand can't be supported.
2) You have a high resistance connection on the battery lead to starter or battery negative leads to chassis/chassis to engine block.
I would immediately suspect the former if battery a few years old but no harm checking the battery connections for corrosion.
Note the volt drop you measured at the starter motor when its not operating is irrelevant until the starter is operating!
