Killing the foxes won't cure the problem, as others have said, the greater availability of food will just allow others to grow to adulthood and replace them.
The only way to entirely remove the urban fox population is to remove their food sources, so no food left out in bin bags, no uncovered waste bins, no unattended BBQs, no fully secured chickens. You would basically starve them out of existence.
That is however very easily said, but the reality is that keeping all food this well away from them is down right impossible. If we could get this to work, we could have used pretty much the same mechanism to get rid of rats, and that hasn't worked over the last few thousand years.
In this scenario all you can do is come back with an even greater degree of security to keep the buggers out.