Nathan Critchlow-Watton wrote in message
.. .
Our house is a ground floor flat, in an 1830's cottage.
The bedroom has two damp patches on the wall, at head height; they
correspond to the position of two cast-iron air vents on the outside
wall.
The bedroom has been damp before we bought it, as the wall below the
picture rail has been de-plastered and covered with 2x2 and then
plasterboard (although from outside, it looks as if there was a layer
of hardboard first?). I think a historic damp problem might be why
the vents were installed.
As the air vents (8" x 6") are under an arch, no rain can reach them,
and there is no sign of water running into them.
Consequently, I assume that the damp is caused by moist air coming
through the vents and condensing on the back of the plasterboard: the
damp is only around the vent (i.e. on the inside, you can see the
outline of the vents on the wallpaper).

Would it be best to (initally temporarily) block up the air vents? If
I do that, should I open up a couple of ventilation grilles into the
bedroom, to ventilate behind the plasterboard?

I'd block them up permanently and just use the windows. They probably date
back to the time when coal fires would fill the room with smoke and you
needed plenty of ventilation.