I've come across it a few times.
In a room with a gas appliance that was not room sealed and required an air supply. I guess the idea of putting it behind the radiator was for aesthetics, diffusing any draft, and to prevent someone sealing it up.
In a conference room I did some work in. The room had an extraction system in the ceiling and the replacement air came in from air bricks behind every radiator. [They were known as Black Hole Ventilators (See here
for website) they had an internal baffle and were supposed to be less susceptible to drafts when it was windy.] The idea was that the air was warmed by the radiators before entering the room. In practice it worked up to a point, but once the room was being used, the radiators went cold because the heat from the occupants turned off the thermostat and then there was a cold draft around the floor and lots of complaints of cold feet and legs. After 5 years the air bricks were filled in and a ventilation system with heat recovery installed.
I would have thought opening the windows would suffice, as they can just be cracked open slightly as and when required, or increase the insulation on the cold surfaces, so that moisture doesn't condense on them in the first place.
Storage heaters are not ideal for bedrooms because of their lack of control can make it too hot, so they tend not to be used, meaning that the fabric of the room doesn't get heated. You may find that once you have radiators installed with proper thermostatic control you won't have the problem. [As long as the radiators aren't used for drying washing]