After some Googling, and manually downloading and running the update, I managed to get the actual error message 1603 from the manual installer. Later I discovered that the generic error "1603" implies a "Fatal error during installation.".
The Microsoft KB seems to indicate that "These errors codes are usually caused by a corruption in the .NET Framework installation or by an inconsistency on the MSI database state.". In an attempt to resolve the issue as per the KB, I attempted to manually uninstall the .net framework, but this too failed.
I then downloaded the un-installer (Refer 3 below) and forced the uninstall. Installed the latest .net framework and updated. I had to reboot the machine after the first lot of updates, and attempted Windows Update again after the reboot. Uninstalling and re-installing the .net framework appears to have resolved the issue.