Local lockdowns aren't working. The North has proven that. Why would it be different in London or anywhere else for that matter? People have stopped complying. They did it in March when it was implied by Bojo that it was going to be a 3 month thing, but as it has become abundantly clear that that this is going to be a way of living until there is a vaccine, and there is no guarantee on a vaccine, people have just said sod it then, I'm not living that way.
I won't be complying. I'll be continuing to see my mum and my sisters. I'd obey it to the letter if it was a 2 week circuit breaker, but as it's clear we're going to have to live this way until at least next Spring, no, I won't be complying.
And for those who say "oh well that's why cases are going up" - until this government kicks itself up the arse and gets a functioning test and trace system in place, they always would anyway. Either it's lockdown or it's cases rising. And most of us aren't prepared to live without seeing family or friends (yes, indoors!) until Spring.