There is simply no magic one size fits all for this conversation.
First things first if you want to cut heating bills then you need to understand how your house loses heat and how much ( a proper heat loss calculation will tell you)
You also need to understand how you use and interact with your house. (This is information any heating engineer should be skilfully extracting from their clients)
You also need to take on some interesting physics along the lines of it takes more energy to heat a litre of water from 5 to 50 degrees C than it does to maintain it at 35 degrees C and then top it up to 50 degrees when needed. (Obvious caveats here - how long are we storing it at 35 and how quickly does the environment its stored in allow the heat to escape.)
Its the first and last of these three things which can be manipulated to increase the overall efficiency of a heating system.
In terms of heat loss we can insulate better and this is a massive help, but if you live in a Victorian town house with single glazed sash windows then just accept your gonna need more gas!
Interaction is a complex one, if people are allowing certain areas of a house to become cold (spare rooms etc) then this can affect the heat loss calculation as generally any heat loss calculation would assume a spare room connected to say a bedroom, that spare room would be at 16 degrees C or even 18 degrees C. Therefore if your spare room is down at 5 or 6 degrees or lower then thats the equivalent of turning your poorly insulated internal bedroom wall into an externally facing wall.
As can be seen from the point above physics controls how quickly a space looses heat and consequently how much heat must be put into a space to maintain or heat it. if we have an internal space surrounded by other internal heated spaces (all sides and above and below) then the heat required will be alot less than if that same space is surrounded by the unheated cold outdoors (think shed or unheated garage in winter)
Historically heating boilers were either on or off and they output heat at a pretty fixed temperature depending on what position the rotary knob was set at on the front. The boilers themselves were massively inefficient usually due to the incorrect ratio of air and gas being burned.
In laymen's terms, if you put a £100 of gas into an old non condensing boiler you would achieve roughly £45 to £55 of useful heat into your house whereas when running efficiently that same £100 of gas put into a modern condensing boiler will achieve roughly £83 to £95 of useful heat into your house.
Modern boilers and controls allow further efficiency by modulating the heating water flow temperature around your house depending on the external temperature. Remember our heat loss calculation - with this we understand how much heat in KW or Btu's our house needs to maintain or increase temperature for a given set of environmental variables (outside temperature and the known rate at which our house looses heat)
Using our modern controls we can increase or decrease the boiler flow temperature, when its say 14 degrees externally we only need a low heat to be circulated around our system to maintain or increase the internal temperature as the heat loss from our house is relatively slow and small. However when its -3 outside modern controls will automatically increase the boiler heating flow temperature to maintain or increase our house temperature.
When installed properly and set up/used correctly modern smart controls will run a heating system to an optimum, however they can only do this if all the above factors have been taken into account and they cannot predict the chances of some glorious winter sun streaming through the windows providing a reasonable solar uplift to internal temps an hour after said controls have heated the space!
I fully understand why some people prefer to tinker and constantly turn up / down the heating (usually the older generation cos thats what we did) but in a well understood house with modern controls the heating can be left to its own devices and provide a comfortable user defined temperature 365 days a year with likely over the long term the most efficient use of gas.
If one day a 'tinkerer' turns up to high a radiator to heat a usually unused space and accidently leaves it on high or opens a window and forgets the heating is on then any perceived savings are gone.
The full evolution of smart controls will see individual radiator thermostatic heads (TRV heads) replaced with smart thermostatic heads which will provide even more control and effectively change single zone heating systems into multizone heating systems where individual room temps can be monitored and heat maintained or lifted as needed to run a heating system in the most efficient way possible.
Well that's enough rambling from me, and of course these are musings from my understanding and opinions so any professors out there who wish to dismiss my musings please do so