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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.
Soul-
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
Maybe more for the DIY thread, but anything I should be concerned about building a pizza oven type thing adjoining a house wall? I'm assuming the heat will all be contained within the brick/plaster and the exterior isn't going to set the house on fire etc.
Yes I could just build a solid shelf and get a pair of roccbox/other but I don't want to have to bring something inside after use/leave it to rust outside.