What to grow under my tree?

More questions before there are any answers, I'm afraid 

which way does the sun travel? I mean does the area get any direct sunlight at all? is the tree deciduous, allowing light through until the leaves grow? Sorry but it makes a difference 

Sounds like the area at the end of your garden is pretty dark and shaded, so you are really looking at a spring-time woodland garden - hellebores, snowdrops, primroses and the like.  Really anything that comes up and flowers before the leaf canopy makes the ground beneath very shaded and dry. 

Another alternative would be to put landscape fabric down and cover with gravel or bark chippings to make a shady seating area for the summer.  You could then grow some plants in pots towards the front where they get more light.  That would give you more options on what you can grow 

my darker corners are either filled with "utility" items such as compost heap or log piles for wildlife and a hedgehog feeding station or rhubarb. In your case perhaps ferns or hostas would work and give a variety of colours if chosen well. Would need a lot of watering as tree will be  a rain shadow as well as sun shadow and will be greedy about taking its share of goodness from soil. What about a statue or water feature
R

Bulbs that are already growing in pots and potted hellebores are easily available and would give you colour very quickly.

Just take a minute to plan what else is going where, to save having to move them again though 

Thankyou guys, like you say, ill take my time and plan for next year in regarding to sping flowers.

Appreciate your advice