"... my garden as it is quite small 6 metres by 4 metres ...."

Firstly forget about an apple tree, grown as a tree.
Think rather growing apples trained as Espalier or Cordon

http://www.bbc.co.uk/gardening/basic...g_apple2.shtml

http://www.which.net/gardeningwhich/.../training.html
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David Hill
Abacus nurseries
www.abacus-nurseries.co.uk