My Wi-Fi isn't unlimited and I need to block any automatic updates. In phone update screen, there is an option "Automatically download updates if my data settings allow it". Unchecking the option prevents download through mobile data, but what about automatic downloads through Wi-Fi?
No it doesn't over the WiFi. But it does on the data connection.
Although if you are talking about app updates you can disable automatic updates from Store's settings and manually update apps when you are on unlimited data.
Automatic OS updates can't be prevented on WiFi at the moment.
Go to Settings >> Background Apps >> Phone Update
Turn Off Phone Update