Thanks for the replies which all make sound sense. I can see that, if heat is required, the engine will need to be on. One thing that has occurred to me is observing Toyota Hybrids. The new range claim that they can (as opposed to will) run for up to 4 miles in pure EV mode and can reach 70 mph.
There are a lot of Toyotas near me as the main dealer is only 5 minutes away. The Hybrids do seem to operate in EV mode automatically when moving from a standing start. Have they all got the climate control off? Is it possible to use residual heat rather than turning the engine on. My feeling is that, if I bought a Mk4 Jazz, the engine would rarely be off except, say, when the ambient temperature is higher than the setting chosen.
Having said that, I guess the petrol engine would only be idling so I may be overthinking this!