Make sure you that the account you are using (admin or other user account) has the priveleges to do so.

you can check the rights for changing the website by going to your account (in the back-end) and then check if you have selected the following for your account (access rights).

website    -------> Manage website and qweb view

after changing the above. Just go to your website and refresh the page.
now you should see the edit button on the left top of the screen.

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Same Problem. I changed Access rights and still no EDIT Function. Ironcially, the other option than:

website    -------> Manage website and qweb view

Is

Display Editor Bar on website

Now that's crystal clear... and STILL no EDIT function.

Had the same problem, solved it by doing an upgrade on the Website Builder module:

Navigate to: Settings -------> Modules -------> Local Modules -------> Website Builder -------> click "Upgrade"