If you have a plugin changing urls to https, that is likely due to it being a bug in the plugin. If your host does not support DSL, you should not have any Ssl pages on the site.
It is happening through the wp-admin/update.php file.
Does it happen if you deactivate all of your other plugins?
Yes it does.
The error looks like this
Warning: An unexpected error occurred. Something may be wrong with WordPress.org or this server’s configuration. If you continue to have problems, please try the support forums. (WordPress could not establish a secure connection to WordPress.org. Please contact your server administrator.) in /home/******/public_html/wp-admin/includes/plugin-install.php on line 77
But on several different files that have a code like this:
$url = set_url_scheme( $url, ‘https’ );
that if I change to
$url = set_url_scheme( $url, ‘http’ );
does away. I did use the Beta tester plugin that updated the site twice a day but then stopped when these errors started on April 14th. The last version it updated to was WordPress 3.9-RC1-20140413 so I updated via FTP to 3.9 but the problem still exists. My host does not allow Apache to have https connections.
My host is canadianwebhosting.com