It looks to me a bit like it was something straight off an architects plan, with those tree planted in a poor position, straight from the concept drawings.
I've seen similar turned into very nice gardens though. Particularly like the scaffold board terrace idea. They are about £13 each, if you are lucky you can get them freebies hunting around builders yards etc. We got a load from a hire company who said they were too old to hire out. They even delivered them for not very much money.
Beechgrove garden television programme have done a couple of makeovers for plots with similar conditions as yours i.e. sloping, dry, under large trees. I believe that there were at least two similar scenarios in the last series, they do fact sheets on their website but I'm afraid I couldn't find them for you if you have a look you may find them.
Looking at the photos,the slope is too steep to use scaffold boards. You would need something a bit meatier like sleepers which are bit expensive. The cheapest option is to dig it over, even out the ground and plant lots of ground cover stuff. Go round all your friends and beg plants. Us gardeners always have plants to spare!
'Optimism is the faith that leads to achievement' - Helen Keller
The post I put on yesterday has not appeared (we had a power-cut just as I pressed the key). Patsy and others are right. For me nothing short of complete clearance would do, so get some mates round with picks, a crowbar, bowsaw, spades and loppers and an old axe and offer them as much tea and food as they can manage, with a beer at the end, and set them to work on digging out all the stumps, including the remaining tree, which will outgrow the space very quickly.
Then you will have a blank space to develop, and things will seem much better.
May I recommend geranium macrorrhizum for the front of your border if you are going to go down the hardy geranium route for ground cover. It is semi- evergreen so you aren't left with bare patches in the winter, and the foliage smells interesting.
You could build a rockery, the rocks will stabilise the slope and provide pockets for soil. My dad used to be able to find cheap stone for that sort of thing - I have never tried so can't advise where to look.
Plants for rockeries (mum used to grow alpines and heathers) might be quite expensive but well suited to shallow soil conditions and they tend to spread out quite nicely over time so it might look a bit bare this year but will mature nicely. I seem to remember some of the alpines you could split at the end of the season and make a new plant or 2.
Not really something I've thought about for years, I just remember that good rockeries usually seem to be on hills - maybe they are out of fashion these days?
Actually, that might be a stupid idea - rocks over tree roots probably isn't good for the tree.
Posts
It looks to me a bit like it was something straight off an architects plan, with those tree planted in a poor position, straight from the concept drawings.
I've seen similar turned into very nice gardens though.
Particularly like the scaffold board terrace idea. They are about £13 each, if you are lucky you can get them freebies hunting around builders yards etc. We got a load from a hire company who said they were too old to hire out. They even delivered them for not very much money. 
Beechgrove garden television programme have done a couple of makeovers for plots with similar conditions as yours i.e. sloping, dry, under large trees. I believe that there were at least two similar scenarios in the last series, they do fact sheets on their website but I'm afraid I couldn't find them for you if you have a look you may find them.
Looking at the photos,the slope is too steep to use scaffold boards. You would need something a bit meatier like sleepers which are bit expensive. The cheapest option is to dig it over, even out the ground and plant lots of ground cover stuff. Go round all your friends and beg plants. Us gardeners always have plants to spare!
Don't forget school fairs and car boot sales for cheap plants.
Craig,
The post I put on yesterday has not appeared (we had a power-cut just as I pressed the key). Patsy and others are right. For me nothing short of complete clearance would do, so get some mates round with picks, a crowbar, bowsaw, spades and loppers and an old axe and offer them as much tea and food as they can manage, with a beer at the end, and set them to work on digging out all the stumps, including the remaining tree, which will outgrow the space very quickly.
Then you will have a blank space to develop, and things will seem much better.
You could build a rockery, the rocks will stabilise the slope and provide pockets for soil. My dad used to be able to find cheap stone for that sort of thing - I have never tried so can't advise where to look.
Plants for rockeries (mum used to grow alpines and heathers) might be quite expensive but well suited to shallow soil conditions and they tend to spread out quite nicely over time so it might look a bit bare this year but will mature nicely. I seem to remember some of the alpines you could split at the end of the season and make a new plant or 2.
Not really something I've thought about for years, I just remember that good rockeries usually seem to be on hills - maybe they are out of fashion these days?
Actually, that might be a stupid idea - rocks over tree roots probably isn't good for the tree.