Will I have a problem heating the large open areas using radiators?

Will the heat just go straight to the ceiling? A friend mentioned
using ceiling fans to counteract this - would this be possible?

If you really can't install underfloor heating, consider using a fan
convector instead of a unforced convector (radiator).

The underfloor will be best, as it will reduce convection, promoting the
most heat low down, where it is more effectively promoting comfort. Failing
this, the fan convector will at least stir the air up, preventing all the
heat going to the ceiling. A ceiling fan set to blow down can also help.
Don't install any fans in rooms that will be heated by open or gas fires, as
they can affect the ventilation, causing poisonous carbon monoxide.

Christian.