The public opinion being in favour of detecting CSAM does not necessarily mean the public opinion is in favour of sending all your photos to GCHQ to check if they're CSAM.
Maybe not, but even the more mild option of Apple/Google doing a local scan of the device, and then secretly sending some sort of result to Apple/Google to take some action, is also pretty awful from a privacy perspective.
Given that according to the last question on that survey the public also overwhelmingly (~90%!) supports holding senior managers personally accountable and punishable by law should firms fail to comply I think it's fair to say they want authorities to have the ability to enforce these measures. The GCHQ has nothing to do with it.
If you ask people "Should CSAM be caught?" they'll say "yes" because, duh.
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".
