Ivy - hedera helix varieties, the smaller ones, but you'd need to heave it out every couple of years minimum, pull it in half and replant, otherwise it'll take over completely.

Would Gaultheria procumbens work there Bamboo? Or a prostrate juniper

Vinca minor. There is a variety called 'Illuminations' which has yellow splashes on the leaves if you want permanent non-green colour

Small ivy, small ivy, small ivy. You should see how much small ivy my garden has, and increasing Bamboo. Very excellent though. And variability of foliages to be enjoyed. Perfect leaf quality 12 months per year, a never ending dependable mainstay. I'm all for them. I had thought of Gaultheria, but needs acidic conditions. Its a good choice. But I have found Vinca Illumination only succeeds in the sun. Have you had success with it in shade Andrew? Superb plant. I have them in baskets too. How small a space can a prostrate juniper grow in? What sort of volume? Do they take shade? And are they happy in alkaline soil?

Hi Jonathan have you considered Heucherella such as 'Sweet tea' it is evergreen and ticks all your boxes?

Hi There, I have as a matter of fact, but only in a quite sunny position and it slowly died, perhaps due to too much sun. Do you think in full shade it would do better? Wouldn't be evergreen though, but yes, a lovely thing. I think I can get it from Crocus. Have you found it attractive in winter?

They are classed as evergreen and have found it attractive over winter Jonathan as it keeps its leaves and colour. Its been in full sun since planted in spring 2010, these plants do well in containers, they must have good drainage, but avoid using thin metal ones as they may bake the roots in summer and freeze in winter.
I have just put a blog of all of my Heuchera and this Heucherella if you want to have a look?

Mine was growing in the ground. I'm mystified then as to why it died.

Lots of things can make an individual plant fail J. My 'Sweet tea' heaved out of the ground, I notice it in early spring and gave it a thick mulch to allow the roots to grow in to it and its fine again now.

Mine got eaten by the roots. :0(. Dreaded vineweevils......

My vinca is grown at the back of a border where next door's weeds kept coming up so it's not getting much sun there

Never seen a vine weevil grub, only the beetle. Glad to know 'Illumination' is versatile. I highly value them.

There's always trailing Nepeta - Glenchoma hederacea (I think that's what it's called - here it's called incense plant). It's much used in hanging baskets in summer, but as long as you make sure you have the hardier variety it should survive well from season to season. I am always surprised to see it, still with leaves, in pots once the summer annuals have long gone.

Shame about non acidic conditions Jonathan, as I think there are quite a few more we could suggest.