Tried loads of things, including running the configuration routine from the command line using psconfig and also stopping the upgrade job and restarting using
stsadm -o setproperty -pn command-line-upgrade-running -pv No(this worked for me in the past when the configuration job failed).
In the end, it was a comment at the bottom of the following page that solved the issue: http://social.technet.microsoft.com/Forums/en-US/sharepointadmin/thread/e3a38087-944b-46aa-b6fa-37482144545b/#page:2
It suggests to remove the WSS Help service from Operations in Central Administration before running the configuration wizard. I decided to ignore the bit about not needing to run psconfig because it tends to log better results during a problem, so ran the following command after stopping the Help service:
psconfig -cmd upgrade -inplace b2b -force
I then ran the normal config wizard to make sure and restarted the WSS Help service in Central Admin....