Google Cloud Translate API - Your client does not have permission to get URL /language/translate/v2

[Zenonas]

I'm trying to make a request to google cloud translate:

$res = $this->request(
            'POST',
            'https://www.googleapis.com/language/translate/v2?'.$queryUrl,
            $params,
            array("X-HTTP-Method-Override: GET")
        );

However, I'm getting a response that:

That’s an error. 
Your client does not have permission to get URL /language/translate/v2 from this server.
 That’s all we know.

The same code on a different server works without problems. I didn't setup any restrictions for api key:

What could be the possible causes for this ? Can the request be blocked by the server and how should I check it ?