Outlook can be fussy about macro security and it seems probable that your system's macro settings may be blocking the code. One possibility is to use selfcert.exe (in the Outlook application folder) and use it to digitally sign the macro project (from the VBA editor - Tools > Digital Signature.)

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Graham Mayor - MS MVP (Word) (2002-2019)
Visit my web site for more programming tips and ready made processes www.gmayor.com

Hi Graham,
I was just about to write to you to say it hadn't worked, but then started to look at other security settings. After having added the certificate, it seems I needed to restart Outlook (when I closed Outlook I was prompted to save the VBA project). When I restarted I got an alert about the electronic signature, and after I accepted it, it started to work again.
Thank you again for being so generous with your time and knowledge!
Paul

Hi again,
How can I add a CC address to the mails that are sent my this macro?
Also, if I edit the macro, do I need to self-sign it again?
Thanks,
Paul