Increasing the insulation will do the job. The real problem is the fact that your nice warm air in the room does not warm up the wall behind the dressing table. Its a very common problem in bedrooms, behind the headboard, when it up against an outside wall.
With better insulation, the cold wall will not be so cold so will not suffer so badly from condensation. The next problem is that the room will now be losing less heat, so the heating is turned down. This leads to this corner still being the coldest part of the room and so would still be the most likely to suffer from condensation.
The real solution is to make this corner thermally part of the rest of the room, say with a fan. This is clearly not practical. You could try to encourage the air to circulate better, such as removing any modesty panel to allow air to get to the wall, or raise the dressing table of the floor with blocks to allow air to get under it. A very low wattage (and safe) heater, say 10 W might be enough but I can't think of one ( fish tank heater?).
A passive heat conductor might do the trick, such as a strip of aluminium that goes right around the corner and sticks out say, 6" from each end. The theory being, that the ends of the ali, get warm from the room so this heat is then conducted right behind the dressing table causing convection air currents which could be enough to clear the condensation.
I have actually used this method with great success. Imagine a long thin kitchen, across one end there is a 2m wide double glazed window. Because the window would not fill the vertical space above there was a long thin single glazed pane, say 2m long and 6" high. In the winter the single glazed pane would get misted up. I put in a long strip of ali, covering the top of the double glazed window frame but extending about an inch beyond it. Because of its height, you did not notice it because you were normally looking at the edge of it. Worked like charm. But I do not think its right for this problem.
You said that you use a woodburner in the room underneath. I wonder if you either put a large piece of ali under the carpet with a decent turn up on the two edges next to the skirting board, it would pick up a bit of extra heat from underneath and direct it to the wall?
Do let us know how you cure this problem, there are millions of homes suffering the same fate!
Frank