Jester2k's advice is good and this is my preferred method of doing it but I just thought that a brief explanation of what is happening may help you.
If you drag a file from one drive to another the default action is to copy it. You can over-ride this by holding down SHIFT when the file will be moved. If you drag a file to a different location on the same drive it will be moved. You can over-ride this action by holding CTRL when it will be copied. If you drag a program to a new location then the default action is to create a shortcut.
I actually meant right click the file and drag it holding down the right button. When you release the right button you'll get a menu asking Copy Here or Move Here. Left click the choice on the menu and its done.
Download a copy of PowerDesk 5 from the PCA download page at: click here
So much better than Windows Explorer. I don't use windows explorer at all now. If you are shifting files from one folder to another on the SAME hard disk Powerdesk automatically "moves" them by drag and drop. If you are going from one hard disk to another hard disk then they are "copied" but you still have the right click option. Personally, I always use the "copy" function in case anything goes wrong. Once I have checked the copy was successful I then delete the originals. Takes a bit more time but "sooner safe than sorry".
When moving a file from one drive to another can be a very risky business. It can go wrong and if it does then you can lose the file. I always use the copy function when moving from one drive to another and when done I then delete the original file. I only use the Copy option when moving from folder to folder on the same drive.
Yes, I did as you said and it works as you say (of course). A new string to my bow! I have up to now been copying over then deleting the old one. All this has been so far on the same drive but with new memory coming to go into my media bay on the Dell laptop, and a new portable HD I shall copy over then go back to delete as is sensibly suggested by Audeal.