urkani on "Connection error when looking for plugins, themes or using the import tool."

Hi guys,

I've just started looking after a WordPress site for a client, and if I try any of the things in the title of this thread, I get the following error:
'An unexpected error occurred. Something may be wrong with WordPress.org or this server’s configuration.'

On the WordPress Dashboard I'm getting the following error in the news section:
'WP HTTP Error: 10060: A connection attempt failed because the connected party did not properly respond after a period of time, or established connection failed because connected host has failed to respond.'

The site is http://www.asbestosafe.co.uk and I've already tried the following solutions from previous threads to help the situation:
Disabling all plugins
Editing my hosts file with the following line - 72.233.56.139 api.wordpress.org
Switching back to a default theme

However, none of these steps have worked. The dashboard also goes very slow, though that's probably a symptom of this problem.

Could anyone help out with this?