Many of the small Vinca will do well in this situation. other shade lovers are Ajuga which keep their leaves all winter and there are some lovely colour variants.

Mimulus doesn't trail but it does self seed and comes back year after year. It loves a damp spot.Nice, but it needs to be in the sunnier part of your "part shade"

Lysimachia nummularia, known as creeping jenny. There's also a form with bright green leaves

Have a look at Cornus Canadensis if you have a slightly acid soil. You will not be disappointed.

Take a look at Creeping Thyme. It comes in lots of fun colors and yes you can eat it. It releases a pleasant minty aroma when stepped on too. Another one I really like is Creeping Phlox.

I think thyme would struggle in part shade - it really needs full sun and a well-drained soil

Thank you all for your recommendations, will definitely look into them all. Like the look of the Cornus also the creeping Jenny. Many thanks

if you want creeping jenny I can send you some. I have quite a bit of it in the garden. send me a pm.

Lovely thank you seaburngirl. Will send you a message. Many thanks

I like water forget-me-not Myosotis scorpoides. It does the opposite, but very pretty and semi evergreen too. Plant it in the shallows, and it will creep upwards covering your pond liner.