I thought the whole point of a thermostat was so you could set a suitable temperature and walk away. If your house is over this temperature say 18 degrees then the heating stays off, if it falls under then heating comes on, it self regulates. This has to be the most efficient way of doing it or why would all modern boilers come with a thermostat? and why would all the recommendations from places like British Gas also recommend thermostatic valves on radiators?
The only way a thermostat becomes less cost effective is if you set it too high say 25 degrees knowing that it will constantly run cos realistically you are unlikely to hit this temperature in older houses.
I leave mine between 16-18 degrees depending on outside weather and what I'm doing, housework can be quite a warming task. If I do get cold then I may just turn it up temporarily then once I feel nice and warm I turn it back down.
It may also be worth getting loft and cavity wall insulation checked/renewed. We had ours done earlier this year and it really has made a difference with heat retention in the property.
The energy saving trust website is good for advice and I actually called them to ask advice and found them really helpful and personable.
I'm obviously not a boiler expert but on another note, if you're at home with a young baby and you know that your house suffers damp and mould, these things do get worse in wet/cold weather conditions so running the heating for that alone and not taking cost effectiveness into account at all has to be done imho.
I just re-checked previous posts and would say I am rather concerned that LL refuses to believe there is a problem with damp/mould. The fact he's bought a de-humidifier for the property means he must acknowledge something, but I think he is trying to fob you off. I really can't think of any lifestyle that would need a 24 de-humidifier unless you like to continually pour water all over your carpets until they are soaked - not!
If he is a private LL I would maybe seek advice from citizens advice bureau or even the council environment office might be some help because that can't be healthy for your baby.