Hi skatemate! You can buy young trees from any dedicated garden centre not so much from the DIY type. There is a place called an Arboretum, they grow trees for scientific purposes and sell them as well. Garden centres and nurseries sell young deciduous trees (the ones that lose their leaves in the autumn) as ornamental additions to your garden. They can cost from 5 pounds upwards.
Why not grow a tree from scratch
Collect some acorns, conkers and chestnuts. Should be some around this time of year. Then recycle some plastic bottles as planters. Cut about 15cm off the top and put in about 15cm of ordinary soil inside, but not clay soil as the new roots find it difficult to push through this kind, add a little compost if you want to (peat free of course or homemade if you have it) but not too much the seeds don't get this in the forest! Make sure the soil is wet when you push the seeds onto the surface and don't forget to put some holes in the bottom at the side for drainage. Make sure the holes are not blocked when you put them outside and not in full sun.Try to forget about them, only check to make sure they're not too dry or too wet. If you think about it squirrels plant trees all the time, they forget where they put them[:'(]
Look around. you may find a tree seed that has germinated already. You can help nature along by planting it the same way as above but plant the root carefully while you do it. I know they will take a while to grow but after one year the growth is faster and if you succeed they will be around longer than you! Good luck!