Only a little bit of damage there - its possibly wind burn. A neighbour had it very much worse than this a couple of years ago and i thought they would never recover, but they did and now look OK. Don't worry unless it spreads and gets worse.

Could also be a local tomcat marking his territory although I don't find goldcrest to be a very tough plant and I've seen lots of them just turn brown and die for no obvious reason

That low damage is absolutely typical of a cat spraying. The colour of the foliage is distinctive, grey or blackening rather than dying off through drought or weather damage.

Thanks for replies.

I did not think of a cat spraying. If its that and I put up a wire fence around the trees, is the damage serious or will it recover when it stops?

I had a Goldcrest Cupressus which had brown bits on it and I just cut them out and tied something round the tree for a few months after which the tree recovered and kept its shape. An old tree man said he would use a stocking or a pair of tights to tie fir trees.

Never thought of cats - much more convincing for that position.