Thanks for your reply, usasma.
With a bit more trial and error I finally found out what I was doing wrong.
When I held down the 'Ctrl' key and started clicking different items on My Pictures to delete them, half the time this would copy them instead of deleting the files that I had highlighted.
The problem was that I clicked the items one after the other too quickly.
When I slowed down clicking the different items - I had no more problems.