Thanks all for joining in with ideas about my "scourge".
I run W2K fully upgraded and Service Patched. I'm on IE/OE 5.5 with SP2 which was a security Service Patch (and includes 128-bit encryption - but that's not a factor here).
I tried going up to IE/OE 6 but found that McAfee's WebScanx.exe wouldn't start and therefore I wasn't protected from e-mails and downloads. So, back to 5.5
Yes, the offending e-mails (and they're increasing in number and are often quite legit) do contain some HTML embedded.
I browsed my MS TechNet resources and found the following somewhat unhelpful document (Q257824) with the advice:
"RESOLUTION
==========
This behavior is by design when the graphic is not included with the e-mail message nor available locally to the computer on which you are viewing the message.
WORKAROUND
==========
To prevent this behavior, choose to work offline in Outlook Express, or delete the message."