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I'd probably be doing this - it looks like lime plaster & mortar, suggesting a solid wall - Condensation / cold bridging is going to be a problem if you are sealing with impermeable materials.
Which could be why the lime plaster crumbled - it looks like it has been skimmed with gypsum at some point - water gets in through holes / condensation permeates the soft brick & mortar, but then can't escape anywhere, and the mortar & plaster suffer.
NotThamesWater
https://www.protilertools.co.uk/product/wedi-tile-backer-board-2500mm-x-600mm--choice-of-thickness---individual-
Being an external wall, an insulated tile backing board would keep the tiles warmer than being onto plaster.
It would mean stripping the wall, so more mess and its going to be more expensive upfront. Though less condensation on the wall and reduced heat loss in the future