Black spots/leaves on evergreen: How do I treat this?

Hello all, 

This is my first post, and problem!

I have a Luma Apiculata growing in a container (evergreen srhub/tree), which I purchased last year. When it arrived it had some black spots on the foliage, which I took note of. Since then the black spots have spread, to cover some leaves entirely. Some of the new growth appears OK, and some appears to be browning already. 

Can anyone tell me if this is the same disease as 'black spot' associated with roses? If so, do I treat it the same way?

I am rather concerned because, at least with a rose the leaves all fall off once a year. This evergreen will keep leaves all year round, so it can always reinfect itself.

I have included photos of the leaves close up, an example of the healthy new growth, unhealthy new growth and an image of the bark.

All help and advice will be gratefully received!

Thanks