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Dumbo
Thanks again everyone - the tanking membrane I ordered was from AKW (same as the shower tray). I emailed them to check whether it would act as a decoupling for the slate tiles too and they said it would.
I did also get in touch with isomat, who were very helpful, but it turned out they'd have to supply a 15m roll of membrane, which is way more than I need, and it would have been expensive to ship to Ireland.
Localtiler - the main reason I was going to opt for cement rather than foam board on the walls was that it can span 600mm studs, which the walls are (I double checked this with the suppliers of the board by email). The walls are already internally insulated and covered in airtightness membrane so it'd be a pain to pull this off to change the stud spacing, but I could do if using the foam board is critical? I can use the foam board on the floor though.
I didn't mean to disregard your suggestion on ditra heat, but I've already got the standard electric underfloor wires and controller connected up (not actually put them in the layer of latex yet though) so it'd be difficult to change now - thanks again for all your replies.