Success! As usual it was something I'd done that had an effect beyond what was supposed to happen.
For months I've been "Spammed" by someone called "Zelda" using the address "Armaggeddon"(sic). To avoid this annoyance I used a "Message Rule" so that whenever an e-mail arrived from Armaggeddon it went straight into the Deleted Folder. Then I could delete it at my leisure. This worked well for months on the NT4 and Win 98 machines using OE 5.01.
When I set up the ME machine with OE 5.5, I went a step further and altered the Rule so that messages from Armaggeddon were deleted at the Server.
You've guessed it; the Rule didn't work as it should and ALL messages were being deleted at the Server after having been received by the ME machine. This is not what should have happened at all.
I'll read up some more and find out how to use this Rule properly. Thanks to those who spent time thinking about this and sorry for the wasted effort.