After getting nowhere with the mokutil command I decided to use the other option and turn off secure boot in the BIOS settings.
I had been loathed to do this because every time I do anything in the BIOS it stuffs the boot order and reverts to booting straight into Win8. Guess what, as soon as I turned off secure boot it did exactly that. Turnng secure boot back on made no difference.
Thankfully, the mailing list archives for this list still contain the instructions on how to fix it.
For those interested, it involved pressing F9 at boot time to select the boot menu and selecting the Centos option. This then went through GRUB as normal and booted. I then used 'eftbootmgr -o' to define the correct boot sequence.
The upshot is that I now have a laptop that boots correctly, and that successfully uses the built in Broadcom WiFi adaptor.
Thanks everyone for your help