Great question..
Some good reading too..
I have spent the last 2 years developing BC skills for city living so here are some hard things to think about. Anyone sleeping out in a city is vulnerable to a number of things, the main one is being robbed. Most cities have an "underbelly" which is pretty dark to say the least so your skills at ensuring your hideout is hidden are your biggest test. You need to travel light, easy in summer but not in winter. Food is relatively easy to get as we live in a wasteful society, there are restaurant bins, supermarket skips and other skips with plenty of food (beware of compactor skips) it's even possible to get out of date medical dressings if you know where to go.
There is always plenty of firewood, but once again if your going to have a fire you might attract people you don't want around your fire, especially if you intend to sleep next to it. Having fires in locked public parks is especially difficult as it may attract the police and then your troubles begin.
Clean water is one of the easiest things to find in a city, at public toilets and as long as you are presentable from toilets in cafes and pubs.
One of the most important things I would recommend for any budding urban survivor would be to be able to adequately defend themselves confidently and by this I mean some form of formal self defense training which includes defense against knife attack, clubs, sticks or bottles.
To be honest the safest and best way to survive the urban environment is to do so on the edge of a city making excursions into the city for necessity but not relying on the city for your shelter and removing the need to have a fire in the city. With cities like London this is hard, but with smaller more compact cities this is possible.
As a lone agent this is not hard, doing it with others, especially a family the obstacles are far greater.
As a final note.. I work in a homeless shelter, a large number though not all homeless people have multiple issues/needs aggravated by mental illness and/or alcohol/substance addictions, on the whole they have a hard time and are on the receiving end of a lot of discrimination for one reason or another, they are vulnerable to exploitation. Some are aggressive, many lead very chaotic lifestyles and see no way out. A few have even done some hard time in the armed services and are maladjusted to civilian life and haunted by their past. The streets are pretty mean, and there is a definate pecking order among the homeless with the stronger praying on the weaker. As a practitioner of BC you should not even feature in that pecking order, but its only a matter of time before the less strong get sucked in. This is where the subtlest skill of all is really put to the test and that is your urban camouflage. Living on the streets without being seen to be doing so. That is the greatest challenge.