You could try Vinca but the soil near a tree is very impoverished. Equally trees do not like to have anything right up against their trunk.

Or one of the macrorrhizum group of hardy geraniums that dont mind poorish soil once they are established.

Thanks for the advice,however i am already overrun with vinca, i would prefer some type of low growing shrub.I will consider the geranium to provide a bit of colour any other ideas would be great .

Ground cover under a sycamore, why not opt for Hypericum Rose of Sharron, when in flower its a carpet of yellow, can be invasive and good for covering large areas, just chop back with edging iron to keep it contained, vinca is good and the varigated form would do ok, also put some clumps of blue/white bells in for spring interest, julien.

Also i have found euonymous fortuni does well in this type of shade, i have one that is planted in deep shade by the side of a very large picea pungens and have encouraged it to scamble up through an ageing budlieja, it does really well and the lovely foliage brightens up this deep shade area, julien.

Just make sure that anything you grow does not get too close to the trunk of the tree.