A few months ago due to mny marriage breaking down I had to look for rented accomadation, and had the same problem... no animals and in some cases no children (I would rather have got rid of the kids than Bailey!!).. NO ONLY JOKIN!!
My arguement was, that they could have a young couple in who could have no respect as it wasn't their house and trash it... whereas I keep my home immaculate and having animals doesn't mean you won't keep a clean and tidy house, probably more so whenb you know it is not yours....
Luckily I found an agent who turned a blind eye even though I offered for him to see my previous house, and the rented house I am in now is cleaner and more up to gether than when I moved in!!!
It really annoys me when pet owners are all tarred with the same brush, most of us are very responsible
Correna and a well behaved Bailey