A few issues with this.
One, some of the behaviours you listed weren't illegal. There were always exemptions for seeing vulnerable people, although certainly those were communicated badly to the public (probably deliberately). The many visits made to the vulnerable people in my family were some of the only gatherings we had that were legal! So data on lockdown compliance isn't going to catch that.
Two, we can't assume people tell the truth about illegal actions. People giving what they think is the 'right' answer to researchers is quite a well documented phenomenon, with obvious implications for identifying noncompliance. I'm entirely convinced that my actions were ethical, but even then I wouldn't have participated in this research in 2020. Nothing in it for me.
Three, you discussed a much longer time period than simply the start of the first lockdown in the post I quoted, and you acknowledge yourself that compliance waned with time. Even by the end of May 2020, still very early days in the restrictions period, the number of people saying they weren't adhering in the LSE research you've posted was 12.5%. Applied across the UK, that's in excess of eight million people. Even at the very start, 5% is over three million. It certainly isn't a high enough number for you to assume that a notoriously animal loving population would've willingly handed their cats over to be culled.
The reality is that some people would and some wouldn't. That was the case with lockdown even from day one, it would've been the case with something most people would've found much more unpleasant.