Thanks for all the input. Just for the record, tonight I did some testing with a DTI instead of the tool and a 3/4 test bar in the taper socket, so I could monitor the actual moves. There was no sign of the problem, everything went as expected, actual tool moves made exactly as the on-screen monitor showed. No sign of rigidity problems (this is a S7, and it cuts perfectly normally under manual control), backlash within expected limits.
This test was done with the spindle stationary; then I tried again with the motor running but clutch disengaged; and again with spindle rotating - everything still as expected.
I decided to try again with a tool and cutting a bit of stock (not my test bar!). One thing I did was to change from "Tool 0" to tool 1 - don't know if that's significant. Anyway, this time it worked exactly as expected, no sign of the previous problem. What was going on I don't know, but it seems to be fixed!
Thanks for the suggestions, sorry this was maybe a red herring, but they made me go back and check everything so for me it was useful.
So a milestone (for me) - lathe/computer combo has made its first unaided successful cut!
John.