In an ideal world sockets are supplied by cables protected from overload at the consumer unit the whole idea of the post war 13A plug and socket was for heating the house after all.
However the 13 amp plug was altered the live pins now have protectors to stop one touching the live pins which has reduced the ability of the pins to transmit heat away from the fuse in the plug. Also the house may have been wired with a ring final but unless tested that ring final may be no more a ring. If on change of ownership the EICR has been completed then there should be no problems.
So for items used for an extended time using 2kW is a better idea as less likely to overheat the fuse in the plug and 4kW (2 Heaters) would equate to just over 17A and the cable is rated at around the 20A mark so less likely of both overheating plugs and overloading circuits.
As already stated not uncommon for extensions to be fed from a 13A fuse in a Fused Connection Unit (FCU) in which case two 2kW heaters could rupture the fuse but it should fail safe.
As to heater types there are three ways to transmit heat, Convection, Conduction, and Radiation. Forget about conduction the electric heaters can use convection or radiation the latter can be both better or worse.
With radiated heat it can travel through windows even double glazed but it does not heat the air it heats what ever it's aimed at. So if there are drafts then radiated heat can heat people but leave the air cold and also is instant hardly any warm up time required. It will of course heat tables, chairs etc which will in turn heat the air in the room but if aimed at some glass will send heat out of the room doing nothing.
With converted heat be it helped with a fan or not it heats the air and so double glazed windows will retain the heat but any drafts will let the heat out.
So a heater like this
aimed correct will likely be better for room used part time but aiming is important likely mounted high facing house not facing any windows. The fan heater because it moves the air will allow heat to be transferred to any cold surface non double glazed windows would quickly transfer the heat outside. If you use something like an oil filled radiator then heat is slower to perpetuate throughout the room so non double glazed windows would not have as much heat on them to be able to transmit it outside.