[imagine how many rats there would be without foxes?]

Well, good question. But, have you ever seen a fox eating a rat? Have you ever seen a fox chasing a rat? Have you ever found the remains of rat that has been eaten by a fox?

I would like to see a scientific study on the subject before making any judgement as to the extent that foxes control the rat population.

My point is that foxes are, in the absence of pre-conditioned and sentimental bias, no more cuddly than rats and I don't think we have moved on from a mind set that was created by the anti-fox hunting lobby.