I had originally used the code given at https://packagecontrol.io/installation to install package manager when I upgraded to Sublime 3. Now although the Package Control.sublime-package file is in Installed Packages, there is no way for me to access package manager (i.e. Ctrl + Shift + P) doesn't give it as an options.
OK, I tried reinstalling Sublime. It didn't change anything, but I then went in and deleted the Sublime Text 3 folder, which contained package manager files and package files. This file wasn't changed during the reinstall. I then was able to start from scratch, reinstall package manager and can now use it properly.