That's news to me that City Fibre have their OWN long distance fibre backbone. Are you sure about that? Never once hace I seen a manhole with City Fibre on it. A lot of these firms that people think have their own network actually just link back into a BT duct.

Well they are building various metro rings

They are indeed, but it's the links between the towns and cities where BT and Vodafone (ex C&W) come in, and to a smaller degree Virgin Media.

But yes of course if City Fibre are building in a specific city it makes sense for them to build out their own network in that area rather than relying on someone else

And operators like Level 3 too

http://maps.level3.com/default/#.U7kx100nJaQ

Yes but Level 3 is all about interconnects between data centres and sub-sea cables. So you'll see their network in big city centres and near where the cables come up from the sea.