Well, having left the thermostat set to 45C thinking it might bring the tap temperature down nearer 60C, I measured the water today at 47C. It's possible to wash your hands under the running hot water alone now, so Mum is happy!
I don't know what temperature the water is being stored at, as there's obviously a heat loss in the pipework, but I'm guessing it can't be far below the recommended 60C if it comes out of a kitchen tap at 47C?
I think I'll tweak the cylinder thermostat up to 50C and work on the basis that the water is probably stored at a safe temperature, but cool enough that Mum's guest will stop scalding themselves when they wash their hands!
Thanks everyone for your help!
you've said you've moved the stat to 45C and 50C, leave it at 60C
you need the stored water to be below the stat to be 55C to kill legionella in the hot water tank, the stat is a third of the way up to ensure all the water above it is at least that temp.
have a look at this
wikipedia - legionella
a ubiquitous aquatic organism that thrives in temperatures between 25 and 45 °C
and
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Temperature affects the survival of Legionella as follows:[21]
70 to 80 °C (158 to 176 °F): Disinfection range
At 66 °C (151 °F): Legionellae die within 2 minutes
At 60 °C (140 °F): They die within 32 minutes
At 55 °C (131 °F): They die within 5 to 6 hours
Above 50 °C (122 °F): They can survive but do not multiply
35 to 46 °C (95 to 115 °F): Ideal growth range
20 to 50 °C (68 to 122 °F): Growth range
Below 20 °C (68 °F): They can survive but are dormant
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if the hot water is 47oC coming out the tap, and as stated, it only loses a few degrees in transmission, your in the legionella growth range
keep the stat at 60oC on the tank,
if scalding is a problem, get a thermostatic mixer valve (TMV) for the hot tap, that reduces the temp right at the tap, not in the pipework / stored water.