The IP you're using to send mail is not authorized to send email directly to our servers.

Symptoms

When sending mail to Google the following error is generated via Exim:

"The IP you're using to send mail is not authorized to send email directly to our servers. Please use the SMTP relay at your service provider instead."

Description 

The error generated by Google references the following article which provides more information:

Google's official docs: 'The IP you're using to send email is not authorized...'

The article notes the following:

"In order to prevent spam, Gmail refuses mail from IP addresses that are not authorized to send mail. The determination of whether or not an IP address is authorized to send mail is made by the ISP that provides you with the IP address. This list typically contains consumer IP ranges offered for dialup, DSL, or other broadband access."

Workaround

Google recommends reaching out to your ISP for a provided solution. The article also notes possible solutions, such as an authorized IP address from your provider or using an SMTP relay.