A friend has said it is because we don't have any cats or pets. We have gotten used to having two of the cats spending time in our back garden but since a new cat has come in there seems to fighting between the cats on a regular basis.

Can't they just share our garden?

I don't think so. I wonder if the new cat is a unneutered Tom too

Its probably dominance hierarchy. Dominance is usually established by fighting, or simply by threatening displays.

This..

In fact in some streets, different cats appear to stick to a morning or afternoon schedule, so that they don't come face to face with each other on a regular basis.