This answer was submitted before the author indicated they were not connected to a proxy or a VPN. I am still waiting on additional information to be provided before I can revise my answer.
After every windows update URL: https://support.microsoft.com/windows opens in my default browser. This only happens on this machine.
The error you have received is due to a network configuration issue. The issue is either connected to the proxy settings of your browser or a configuration issue with the VPN you are using.
The issue occurs when Firefox uses different proxy settings or VPN instead of what is set on your Windows computer. Whenever a website figures that there is something wrong with your network or browser cookies, etc, it blocks you.
This configuration error is due to Firefox using one configuration and your operating system using another.
How do I fix it?
If you are using a VPN, I would try disconnecting from the VPN; if you are using a proxy, I would discontinue the use of the proxy.
Should I bother about it?
You will continue to have this problem until you determine what exactly is wrong with your Firefox configuration.
Source: Access Denied, You don’t have permission to access on this Server
After you eliminate a misconfigured proxy and VPN from the equation, I would reset whatever browser you are using. Since I highly suspect you are using Firefox, I would start Firefox in Safe Mode, before getting rid of your profile. Only after you verify that Firefox in Safe Mode does not solve your problem, I would delete the user profile for Firefox, if you continue to have the problem contact your IT Administrator.
You indicated Windows is not using a proxy, that does not mean that Firefox isn't configured to use a proxy, Firefox can independently be configured to use (or not use) a proxy.
On Windows: Hold the Shift key when you open the Firefox desktop or Start menu shortcut.
However, if the issue is not present in Firefox Safe Mode, your problem is probably caused by an extension, theme, or hardware acceleration.
This error does not seem to happen to any other browser other than Firefox. This means you might be able to solve the problem by using Firefox Safe Mode.
Source: Access Denied You don't have permission to access
Internal office network directly connected to the internet
If starting Firefox in Safe Mode does not help, and even after you have deleted your Firefox user profile directory, you still have the problem. It sounds like that because you are a non-privilege user, you will be unable to solve the problem yourself, and will have to contact your IT Administrator. This problem is only caused by a configuration problem with Firefox.
I don't really care if I can open the URL or not , I'm more concerned why the link opens up automatically.
It happens due to a network configuration conflict between Windows and Firefox. You should contact your IT Administrator to help resolve the configuration issue. This problem cannot be solved by a non-privileged user.