"This, she explained, was because the Act does not tackle the fact that services including Twitter and Tumblr contain hardcore pornography but will not be required to introduce age-checks. "
It's only commercial porn sites that are being targeted. Sites that happen to host pornographic content (e.g. tumblr, reddit etc) aren't included
The relevant section, "a sentence was slipped in that gives a regulator powers to act against sites “making prohibited material available on the internet to persons in the United Kingdom”" - That means any website hosting said content, whether they accept money or not.
From the lords debate on the topic https://hansard.parliament.uk/lords/2017-02-02/debates/D2C24...
"However, I want to mention briefly user-generated material on social media, an issue that naturally arises in debating this Bill if we are told that it will not cover it, despite a vast amount of hardcore porn that can easily be viewed by anyone, including young children, being just a couple of clicks away. "
They mention tumblr/facebook being included but only when showing "commcercial" material, which appears to be the differentiating factor so sites like reddit wouldn't be generally in-scope.
In section 2.1, "All providers of online pornography, who are making available pornographic material to persons in the United Kingdom on a commercial basis, will be required to comply with the age-verification requirement." So advertising funded sites fall outside the remit.