Most of the homeless in my city migrated here from outside of the city (and often State) to come here for our weather, services, and lax attitude towards drug use as far as demographics go. We're a navy town so there's also a tragic sub-group of veterans with mental health issues but the bulk of our homeless (we actually use the term "transient" as side context) don't fall into this category and mainly came here for the conveniences. I'm sure there are some who are trying to "dig out" as you say but it's certainly not most of them and for the ones who aren't trying to do so a bike with charging capabilities would be both a mobility boost (again assuming theft wasn't a concern) and a general utility boost (smartphones are largely ubiquitous amongst our homeless and are actually extremely valuable as tools since they're both navigation aids and access points for online services offered to them in my city). This is why I was asking what the demographics of the homeless in London are like since if they resemble our population then the bike wouldn't be such a terrible idea (but I'm also still unsure about the practicality since while some of our homeless ride bikes most get around via public transit and so just putting chargers on busses would probably be more pragmatic as a service to them).