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Sorry, wasn't very clear - not on the wall, but next to it. There's a side return with a staircase coming down it from a deck above (we live on a hill), so:
wall > space (about 1.5m) > staircase
Was planning on building a solid table/shelf (maybe brick?) and then the oven on top on the staircase side with some work space to the left of it. I guess as per @Gewürzt I could store something like a roccbox outside particularly if the shelf had solid storage. Does rather go against the Devon-terranean aesthetic I was angling for. Will have a look for some shelving inspiration.
CYOA
Soul
Do you mean literally connected to your house wall?
I think that would cause some issues with heat retention in the wall and require some regulations to be adhered to.
You should be ok to build pizza oven close to your house.