I have accidentally deleted a file - is there a way to recover the file? Could not find anything in 810's manual.

Where was the file located? If on a memory card (FAT filesystem) you may be able to recover it with some DOS/Windows undelete utility. I'm not aware of any such tools for JFFS2 so if it was on the internal storage (root filesystem, not to be confused with the internal memory "card") you may be out of luck :-(

The files were on the internal storage and I was trying to copy them to the memory card - I hit the trash can accidentally while the files were selected. There was no confirmation and the files vanished!

If you were using the default File Manager then it should have asked for confirmation, but you may have overlooked it or thought it was the confirmation for moving the file. In any case, I suggest you immediately remove the memory card so that there is no danger of any further writing to it (which will likely overwrite the deleted files), then search for FAT undelete utilities, as lma says.