In response to Steven Brockwell's question, correspondent Joe Micallef identified one of the key issues concerning water heaters; namely, conductive heat dispersal through the insulation which is never 100 per cent efficient.
I endorse his comments as I control my heater via a plug-in timer for when heated water is needed, but I have gone further than his old jacket cladding. I have had a made-to-measure insulating cover tailored from quilt/sleeping bag material to reduce heat losses (see photo).
It is a simple and effective measure to help save energy.