Thank you, britechguy, for the recommendation of IMAP.
Thank you, tristar, for your suggestions. I am open to the possibility that I have caused this problem by an inadvertent moment of clumsiness at the keyboard. Taking your suggestions one by one: I have checked my settings and I have no rules at all; similarly I have no archiving set up. Regarding your third suggestion ('The emails have been moved to a PST or moved from another device'), I do not understand how I could move the messages from another device, as I am a POP3 user; the messages were downloaded to Outlook and were in my inbox. As for 'emails have been moved to a PST' would you mind explaining how the messages could have been moved to a PST, and how I would find them if they had?
Is there a way to search all my Outlook emails in one operation, rather than searching each folder individually? Even if I find the missing messages, it seems to me that the sub-folder into which I tried to move them has somehow been corrupted and (if it can't be repaired) I need to replace it with a new, differently-named sub-folder.
Many thanks again for your help.