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checked that the cistern isn't stuck open for some reason?
Definitely do this.
Some friends renovated their house. The husband is an engineer and very handy so did everything. They were being charged a fortune in water, so they understandably kicked off and got a refund.
Just to be on the safe side they checked all the plumbing only to notice that one of their toilets was constantly flowing ever so slightly and obviously had been for months.
Maybe a silly question, but have you checked that the cistern isn't stuck open for some reason?