We have a woodburning stove/cooker (Esse ironheart) linked up via its back boiler to our hot water system.
It works well tho we havent tried to connect it to the oil fired central heating (which is mainly underfloor).
We made sure it is gravity fed not pumped, so the angles are correct for that to work, pipes wise. It means that since it also cooks, if we have a power cut we have cooking, some hot water and some heating direct from the stove!
In my experience it might be more efficient to just heat hot water with the stove and look for another way of doing the central heating as the input needs of HW and CH are very different (one needs high temp but not all the time, the other needs constant lower temps, wood stoves arent ideal for the latter).
What about solar or heat pump for heating?