It can be done but my opinion is that for a two bed house its just not worth it.
My advice would be to have the heating system 'fixed', block off the fireplace to reduce heat loss and look at other ways of making the house snug, at the same time ensuring enough ventilation.
You can fit a standalone wood burner if you want in the fireplace but there is a lot of work with sourcing and storing fuel and cleaning out ashes, chimneys etc etc.
Have you considered a glass fronted gas fire in the fireplace?
Its possible that the back boiler is still connected to the system and if not done correctly, the back boiler may act as a rad
How old is the heating system?
Has it ever been flushed out?
Does it have inhibitor in the water to stop corrosion and build up of sludge?
Tell us more about it please.