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Why didn't you say so! Sack off your shitty third bedroom upstairs, take the hit in the property value now it's a two bed and make it a proper bathroom, then have a downstairs utility (or something else useful). Obviously.
No idea about regs etc, sorry. I'm pretty sure the concealed cistern I ended up with (one of these) would fit in a 100mm void though. Once it's all feeding off the same side you can concoct some fancy nice bespoke thing to bring it all together.
Rotate loo 90ยบ to towel radiator wall, so the bowl is in essentially the same place; swap basin and towel radiator. Would give a cleaner entrance to the room? Coupled with switching the bath to the other way round, you could then conceal everything in a stud wall and have some nice concealed cistern/recessed storage thing going on.