Possibly a young holly?

Euonymus? A non variegated one ?

I think it is one of the evergreen small leafed forms of Euonymus. I used to have something similar in my previous garden.

A variety of Pittosporum tenuifolium would be my guess.

Just looked at lots of Pittosporums and it does look like tenuifolium.

I have that plant. It's Euonymous possibly 'Green Rocket. Mine is a volunteer but it's just what I needed on the end of the driveway. I like the shiny green leaves against the white snow. They grow very slowly so it only needs 1 trimming for the season. That's all you need to do with it. Mine gets buried alive in the snow, salt spray from the road, drought conditions in summer - always has those shiny green leaves. The key is full sun and good airflow. Not enough of either will result in those horrible spider mites which will decimate the plant. I think it's worth keeping,but that's up to you. They also make an attractive evergreen hedge.

Thanks for your comments. I think on reflection, Euonymous may fit the bill. I'll check out info on it. Seems tough as old boots and as you say v slow growing.