Hi Rob Campbell-Bell,
Good Day. Hope everything's fine. Let's try to do some steps to solve your issue with your emails.
First try to search everything again. If you remember some data on one of your mails, like Sender's name, address, unique word on mail title or message content. It will be better if you'll do this both in your Outlook Desktop App or Outlook web browser.
Second, try to check also Archive > All Mail > Other Folders. Sometimes messages are moved to archive or Other Folders.
Third, if it is not in any folders on your mail, and assumed that this is permanently deleted, try to contact microsoft support in Outlook.com. A support may be able to check your lost emails. Go to Microsoft Support website > Select "Outlook.com" > "Contact Support" choose "Email messages missing or deleted".
I hope one of the options above can solve the issue. Have a great day.
Sincerely,
Jhun