Hello Lloyd,
You must have skipped some required configurations to be done in Fine Tune Activity E-mail and Fax settings --> E-mail and Fax settings.
1. Add your domain/subdomain which you are using under Allowed Sender E-Mail Domains.
2. Choose first option to send the e-mail to Business Partner under E-Mail and Fax Delivery in a Non-Productive System.
3. You can also try testing e-mail send functionality under Send Test E-Mail option under same Fine Tune Activity E-MAIL AND FAX SETTINGS to check if the e-mail sending functionality is set as required.
Regards,
Chandan