Is the moss on the branches or on the soil? If it's on the soil, regular hoeing will discourage it ( a rolling stone, and all that). If it's on the branches it's probably lichen which is harmless and indicates clean air.

We have C. horezontalis around windows and up the wall of the house but have never had this problem. Presumably it must be quite bad as you are asking the question here. I wouldn't advise spraying a moss killer on a plant so, appart from picking it off by hand, I am afraid that I don't know.

The presence of moss indicates that the area is damp and that rain / water / moisture isn't draining away as well as it could.
That would make the moss sit around the lower areas of the plant.
I think you need to improve drainage there because this could be an ongoing situation.

Spike/aerate the ground there, see if that helps short-term ....
longer term though i'd think that digging the ground there (checking there's no builders rubble deep underneath, being the culprit), removing some soil and then incorporating lots of grit might help.

The moss is on the branches and I'd say it is much thicker than lichen. The wall is north facing and we get a lot of rain in Glasgow!!
I'll photograph it tomorrow.
Thanks Linda

I have a certain north facing border and it used to get a lot of moss before i aerated the whole area, i hardly get any there now i've done it.

there are lots of foliose [mossy/leafy] lichens so I will look forward to seeing your photo.