Trapping and releasing is considered very inhumane and may well not solve the problem - in an urban area a new set of foxes would just move in.
There are only two legal methods to permanently deal with foxes, and only one applies to you since you are in an urban area. Legally you can have them trapped and destroyed with lethal injection. However, it can be very costly and chances are the council will not cover it (last time I looked it was in the region of £450 per fox) and it can be hard to find a vet willing to administer the injection to a healthy animal - and only a vet can.
Your best bet is managing your own territory, someone already suggested Scoot and I'm going to second it: Scoot on Amazon.
You may find this gets worse before it gets better, and chances are you won't actually get rid of them, but you may deter them from your garden. If you challenge the foxes (which you will be by using something like Scoot) they may 'fight' for their territory by scent marking and pooping on everything for a while. This should subsidise if you persist.
If you prefer the idea of trapping & destroying then have a look for someone through these guys BCPA. But remember it could be expensive and new foxes could just move in.
Can't remember the poster who gave you the list of how to secure the garden (sorry) but do everything they said and also consider getting a taller, stronger fence.
Your idiot neighbours are not only idiots for feeding wild animals in their garden but also for feeding them bread 3 times a day
this is from the RSPCA:
If you choose to feed foxes, they'll eat meat in almost any form - cooked or raw - and cooked vegetables too. Only put out enough food for one meal, otherwise leftovers may go off and cause sickness or attract other unwanted animal visitors.
so perhaps let your neighbours know they may be harming the foxes by feeding them junk too often.
Good luck with this and PM me if this thread dies - really interested to hear the outcome and if you manage to contain your garden (or if you end up trapping & destroying). Work with foxes (but mainly rural) and find every aspect, good and bad, completely fascinating 