In our garden next to the shed we have a (I cant think of the name, but yeah, a wooden structure thing) which runs up to the wall and up against the wall we have a bit of old trellece which is held up by some timber beams/bricks/odd bits of concrete which is where we keep our stuff which we burn. Its about 2m wide, 40cm deep. We have filled it before this winter and probably have about a quarter left.
For you, all I would do is flag a length running next to the wall, and run some sort of plastic sheet over it, depending on how big the load of wood is you have and then just pick at it willy nilly. Then you can cut the wood so it can fit in your fire, store it and then just chop it up when you need to. We have a chainsaw and axe, and we axe it up probs once a week, we keep a big bag of chopped up stuff and kindle in the shed. You can even store the wood in bigger bits, as I guess it will need to dry out.
PS; if you can, get in with local landscapers/tree surgeons, they might be able to get you ‘better wood’ ie, tigther grain stuff as it burns better, for a more reasonable price compared to places like b&q etc etc. We’re sorted for wood as my dad is a landscape gardener and knows some tree sergeons quite well..