Maybe a Phlox subulata variety? Has it ever bloomed, Littemisssunshine?

My father seems to recall seeing flowers on it. It was in their neighbours back garden, however the neighbour doesn't remember what it was.

Hmmm...if it is in the shade, a Phlox subulata would not be able to bloom. As of now, there isn't enough data. Can you get a close up of one of the stems? You should be able to add the picture to this question, but I'm not sure how.

I've enlarged the photo and added two more pictures. My parents no longer live in that County so we cannot get any more info. Thanks for your suggestion.

This does look like a plant I have in a small wall container. I thought it was a variety of Sedum. It has a small yellow daisy-like flower. This was given to me by a neighbour so I'm afraid I don't know the name either.

I have suggested Phlox and Sedum to my mother, thank you both for your help, much appreciated :)

Aha! I should have thought of that! It is probably a kind of Ice Plant, a Delosperma variety.

Delosperma nubigenum 'Basutoland' hardy ice plant. I have had another look and I think this is it and the flowers seem to match. A bit of a mouthful don't you think.

Thank you both so much ?