It was already in the garden when I bought the house. It has a central trunk with horizontal arms all around with very delicate leaves. Tis very unusual, I love it but would love to know what it is. Does anyone else have one of these?

It's a lovely and ancient species of conifer called Metasequoia glyptostroboides.....or Dawn Redwood. It was only discovered in the 1940's (at least by western botonists) in a remote part of China and only in this area. Sadly, many of the native trees have been cut down for firewood now. My parents have a lovely specimen in their garden in Northumberland.

A friend of mine has two as bonsai

You are very lucky to have this tree, our council has stupidly felled one this winter saying it was dead. They hold their brown leaves for some time in the winter and appear dead.

Oh WOW - a name! Thank you so much all of you. I will learn all i can about it - it's the most delicate looking thing, easily missed among the other planting.