Tested again this morning. Garage below 5 degrees C, but full battery from yesterday's charge.
Immobiliser disarmed in two seconds. So........I'm thinking that this must be battery voltage related. The sensor coil is permanently live, as it has to read the key before the ignition is switched on. My instinct tells me this shouldn't be 12volts, but I haven't tested it. Clearly there's a very tight margin around 12volts whereby any reduction de-sensitises the coil.
I don't see an easy fix to this, other than a fully charged battery.
DaveW '05 Red Roadster S1 '16 Yellow (Not the only) Narrow AR GDI Plus 4