If you ask people "Should phones scan their files for CSAM?" a good part will say "yes" because it doesn't sound like it affects anyone outside of child pornographers.
If you ask people "Should phones send your photos to GCHQ to check if they're CSAM?" most people will say "no".
If you ask people "Should phones send your photos to GCHQ to check if they're CSAM, and should we send Apple executives to prison if they don't make their phones do this?" most people will still say "no".
Let's say the question was written something like this:
> Do you believe it should or should not become a legal requirement for the following to scan messages and posts on their platforms for child sexual abuse, even if such scanning would also compromise the security and privacy of all law-abiding users of the platform?
I obviously can't say for certain, but I think that 60% and 79% would drop, at least some substantial amount. Even if the "should not" positions wouldn't go up, I think it would muddy the waters enough that many new people would fall into the "don't know" camp.
The problem is that the polling just presents these questions to evoke a "oh, obviously I'd want this, to protect the children!" sort of reaction. The "but think of the children!" thing is almost a joke or cliche at this point, but it is disturbingly effective at shutting off people's critical thinking, causing them to agree with whatever the argument is. On top of that, media reporting around these issues never gives the pro-privacy angle enough consideration. And even when it does, it's usually in small "nerdy" publications that most people don't read. I'm also of the opinion that many people just can't and won't understand, adopting the fallacious "if I've done nothing wrong, I have nothing to hide" position.
They didn't, and for what it's worth public opinion is overwhelmingly in favor of the law. I think anyone discussing a British law ought to keep that in mind (https://docs.cdn.yougov.com/68pn2b6b57/NSPCC_OnlineSafetyBil...). Even on the most contentious parts of the bill:
Do you believe it should or should not become a legal requirement for the following to scan messages and posts on their platforms for child sexual abuse?
[Private messaging services]
This should be a legal requirement -> 60; This should not be a legal requirement -> 21; Don’t know -> 18
[Social media sites]
This should be a legal requirement -> 79; This should not be a legal requirement -> 10; Don’t know -> 10
Likewise on E2EE over 70% of respondents agree that ability to access them is warranted. So the framing in the discussion as if this is solely the British government against technologists is completely off, it's also taking a position against the British public.