Admin toolbar and login

Having redeveloped my site using a spare url for testing it out, I have now switched the real url to point to the new site. But a few things have changed :
1) when I go to the site, it used to have the top admin toolbar (with Howdy, etc.) displayed and I would have been automatically logged in. Now it doesn’t, so I have to go to /wp-login and login manually.
2) Even then, when I go to the site having logged in, the admin toolbar is not displayed.

I haven’t changed the user profile selection (Toolbar still checked), and I have changed nothing in the Theme (Twenty Ten).

I am new to this, so please be gentle !