Urban foxes thrive in an urban environment because of their adaptability and intelligence. They rarely need to kill, as they can eat carrion, food waste, slugs and worms. Rural foxes will overkill, but that has a lot to do with food scarcity. The intention is to return and collect the surplus at a later date. Quite often a fox will behead its prey and for some reason takes the head with it rather than the rest of the body. This is actually because it is playing the averages and is more likely to escape successfully with half a rabbit/chicken than lugging a whole one with it. This beheading may be one of the reasons that they have a reputation for gratuitous killing.
Rural foxes come into conflict with farmers because of the coincidence of lambing with the rearing of the fox litter. Born in March and now growing at a massive rate, the cubs spend the first month in the den with mum, with the father foraging to feed her as she nurses the cubs. In April they start to emerge and explore around the den, not straying very far, so this is perhaps the best time to see them.
As they grow they will be fed by both Mum and Dad, and potentially other "helper adults". Average litters are between six and eight cubs, and a considerable amount of food is needed. Many foxes don't make it to six months, with food scarcity and competition the biggest factor. Those that do survive will start to forage for themselves and by six months will be on their own. This is another critical time, as they are very territorial. Vixens will be looking for mates, and dog foxes will be wandering about trying to establish a territory. Autumn is therefore another prime time to spot foxes in towns and cities as the young dogs are effectively homeless and tend to be seen wandering the streets. Virtually indistinguishable in terms of size from their parents at this age.
Mating season is midwinter. Depending on the environment, foxes are believed to be chiefly monogamous, but studies have discovered females with more than one suitor in mixed dens. The female is ready to mate for less than a week in January or February , and it is this time that we hear the bloodcurdling screams as she advertises the fact.
Adaptable and not particularly fussy about dens, they will make use of other animals' abandoned earths, and of course in an urban environment they find garden structures and other outhouses particularly useful.
Urban foxes are one of our environmental success stories. They are fascinating and endearing to watch, and apart from the occasional sensationalist baby eating stories they are pretty good at living alongside us. It's come at a cost to them, with endemic levels of sarcoptic mange as one of their biggest enemies. Because they scavange rather than hunt, the conflict is lesser in towns and cities, although there are still plenty of instances of pets such as hens and bunnies being taken by the opportunist Charlie.
My personal view is that the fox in the OP should be humanely despatched. The thought of a slow and painful death because of misplaced sentimentality is anathema personally. Firearms are not the answer however, as the (I assume) urban location means their use would be unlawful or unsafe. Many pest controllers have the means to trap or catch the animal, and it could be that the local council will have access to such a service.