Tbh, the sooner we remove the human from the equation, the better. It's scary to think that we allow so many careless people to drive vehicles that can kill people. I'm not talking just about drunk driving, but all the sort of distractions (smartphone, looking somewhere else, ...).
London specifically, AFAIK after midnight has no tube service. This means that Waymo (or whoever takes a similar initiative) actually helps towards creating a public transportation service that is cheaper and even safer than the current one. I'm personally all up for it - don't tax innovation!
This was solved by taxis, and now uber, decades ago. If you're dumb enough to drive under influence in 2025 the cure isn't a driverless taxi it's 10 years in jail.
It's definitely not a cure, but removing the human factor (aside from the intoxication part) is anyways a very good goal IMHO.
Oh and btw, I've seen also taxi / uber drivers that were under the influence of alcohol / cocaine. Humans are the problem.
If only such things were googleable.
As another comment pointed out, there are a few lines open during the night on weekends, and there are buses.