"Cookies are blocked or not supported" since update to 3.7.1

After doing all of the below I still have the same problem.
– deactivating all plugins to see if this resolves the problem. If this works, re-activate the plugins one by one until you find the problematic plugin(s).

– switching to the default theme to rule out any theme-specific problems.

– resetting the plugins folder by FTP or PhpMyAdmin. Sometimes, an apparently inactive plugin can still cause problems.

– re-uploading all files & folders – except the wp-content folder and wp-config.php & root .htaccess files – from a fresh download of WordPress. Make sure that you delete the old copies of files & folder before uploading the new ones.

Please help.

Disabling all plugins makes no difference. Still the same error.
Disabling all plugins and all themes except Twentie10, 11 or 12 gives me a white screen.

Yes. They confirm nothing changed on their side. What puzzled the engineer, and I know him very well and trust him, was the switching from http://www.domain.nl to http://domain.nl when you open a site. I can see WordPress creates cookies both with and without the www prefix in one session.

I cannot login, therefore I cannot check …. Is there another way?

That is not what I meant. Is there another way to check the url setting, as I cannot use the admin screen to access Settings => general.

OK, I see. So, what’s next?

Any browser, any computer, Android phone, any network. And I have two separate sites that have the same issues. They were both running fine before 3.7.1.