Finding a rental property

I am disabled and was born disabled so I claim pip and also UC, my partner works full time and I have an assistant dog. The council won’t house us because my partner earns to much, and finding a property privately is almost impossible! Most don’t wanna know due to my assistant dog and others due to benefits. Even when you mention the laws regarding assistant dogs and disabilities it’s still the same. Is there something I’m missing?

so much competition for properties, not enough properties due to councils selling off their houses in the past, housing assoc. selling now and extra taxes on landlords, so many selling up