If your maximum use of hot water is around 7- 8 am in the morning and 10 to 11 pm at night – getting up in the morning and going to bed at night – a delayed switch-on would account for the odd timing. In other words, it’s taking your system four hours to catch up with water usage (or whatever …).
So yes, as suggested above, it’s definitely worth getting the hot water system checked. A water leak, a faulty valve or a faulty thermostat might account for the odd and variable bills.
My money would be on a faulty thermostat – but I’m just guessing. To get your agent “interested” tell them if they don’t send a plumber round to check, you are going to seek a rent reduction through Fair Trading to compensate for the excessive payments cause by a faulty hot water system.
Also, if your hot water tank is leaking, this could be a precursor to a tank failure – and a very messy and destructive flood.
Ask the agent to sent a plumber experienced with hot water systems.