Last night, near Streatham Common station, I saw a ginger domestic cat and urban fox within about three foot of each other. Neither seemed to be in the least bit interested in the other, and far more worried about me, even though I couldn't get anywhere near them because of a six foot high metal fence between us!
I've always assumed that there would be some animosity between the two species, or at least avoidance, since they must be targeting broadly the same sort of prey.