I think that's an exaggeration. To take an article at random (
https://www.bbc.co.uk/news/articles/c24v4dl5r16o):
> Chris Sherwood, chief executive of children's charity the NSPCC, said Friday's new rules mean services "can no longer evade their duty for protecting children".
> For Prof Elena Martellozzo, professor of child sexual exploitation and abuse research at the University of Edinburgh, the rules send a message to the tech industry that "child safety and child protection are not optional".
> The Molly Rose Foundation, a charity founded by the family of Molly Russell - who took her own life at the age of 14 after seeing harmful content online - has said stronger legislation is needed to better protect children.
> Derek Ray-Hill, interim head of the Internet Watch Foundation, meanwhile welcomed the new rules for sites allowing porn but said "there is still more to be done".
I think there absolutely is pressure on the government for things like this. Certainly not mass pressure in all segments of the population but neither is the government acting alone.