How high are the bottom branches off the ground?

The first thing that came to mind is shade and dryness!

You can do things for dryness but not with shade!

There is a list of shade/dry tolerant plants here;

http://www.thegardenersalmanac.co.uk/Data/Plants%20for%20purpose/Plants%20for%20purpose.htm

Asuuming the branches are quite high you might get away with some of these!

This article on planting under trees might help;

http://www.thegardenersalmanac.co.uk/Data/Planting%20under%20trees/Planting%20Under%20trees.htm

If sunny, then Lavender can look great-seen it planted under many trees.

Cyclamen corms give colour at this time of the year and can be planted around the base of a tree.

Yew gives the densest shade of practically any tree , plus it is poisonous to various creatures esp horses. That is why such a valuable tree was/ is grown in churchyards, a place not known for horses! Eating the leaves leads to a quick death. All parts of the pacific yew are toxic. Anyway, due to the poisons there is not much that will grow underneath. If your garden is big enough much better to try topiary. Yew is not a slow grower. Given the right conditions it can grow 60cms a year. But to do that it will take up an enormous amount of water. Better to enjoy the splendour of a stand- alone specimen. Much of the yew can be used in medicines, how come the druids revered it, what did they know.
Southportsmith

Many thanks

I would try euophorbia robbiae. Under those conditions it wouldn't spread fast enough to be a nuisance and I would be surprised if it didn't survive. Vinca minor may do either or as well, but it won't be lush!
Otherwise why not just use bark or gravel perhaps with an ornament and some containers which you could use in rotation perhaps a week or two at a time? Begonia sempervirens wold be a good one for that, or you might risk the impatiens New Guinea hybrids which so far appear resistant to the horrid new mildew?