It shows an average COP of 2.5 to 3 for heating water to 50C (not the legionnaire cycle) in mild September weather. That COP figure is likely to drop during colder winter weather and when the need for CH kicks in.
His costings include 5p/kWh for one hour at night (now 12p/kWh for 4 hours duration) but he needs to factor in that he will need CH during the day/evening and that same tariff is 9p/kWh more expensive than the standard variable rate from the same supplier. Give it a few years when more people have electric heating and are charging their EV overnight there may not be a cheaper overnight rate.