If the house was empty all day, it would be more efficient generally to time the heating to come on in the morning and in the evening. The energy you save by not having the heating on for a long period every day is more than the extra energy it takes to heat up a cold house. However, there will be a time point at which the cost of heating a cooled down house balances the savings on fuel if the heating is only off a few hours – what that time point is depends on your individual circumstances.
However, your problem seems to be more that you want to be warm in the house during the day without having huge bills. It makes sense to plan how to do this using the heating system more efficiently rather than being uncomfortable. Keeping the thermostat setting down to 18 or 19 degrees Celsius and using individual radiator thermostats in different rooms help with this. Bedrooms can be kept cooler using lower thermostat settings, or even left cold by turning the valve to off. The rooms that you use can be kept more comfortable using a higher setting. Closing doors to keep the heat in and making sure windows are not left open is also important.
Have you considered fitting radiator thermostats and only heating the room/s that you use during the day? You may need to consider how you use the house during this time to make most efficient use of fuel. If you work at home, using one room predominantly as an office, is it possible to heat only this room? If you spend most of the time in the kitchen, is it possible to heat this independently? A combination boiler has the advantage that it only heats water as it is used, so heating one room rather than the whole house could be cost-effective.
You say your husband is against cavity wall insulation but this is an excellent way to prevent heat loss and so make your heating system more efficient. All modern heating systems with gas boilers are checked at installation to make sure that the air supply is adequate and safe and there is no evidence that walls need to ‘breathe’ or that the air supply in any room is compromised by cavity wall insulation. Perhaps if you found out more details about the process and its costs and advantages your husband might change his opinion. It would also be wise to look at loft insulation, double glazing and other methods of reducing heat loss.
The efficiency of your boiler also needs careful consideration. If it is more than 15 years old, it may have become inefficient. It is possible to fit a condensing combination boiler that is around 30% more efficient than a new standard combi boiler because it reuses heat that is usually wasted. These are more expensive but do pay for themselves in the first few years of use.
I’ve a wood pellet boiler with a large buffer tank in the garage. Is it more efficient to run it constantly or not? The heating inside the house is timed to come on and off at different times (morning and evening) but is it more economic to put a demand on an already up-to-temperature boiler or fire it up from scratch? The boiler is an Extraflame LP20 and house is well insulated.