Condensation is the effect of moisture depositing on the internal surfaces. Condensation occurrs because of the difference of temperature between wall's surface and air inside the building.
Paint and coatings are only a partial answer to condensation.
There are two types of paint products that can help to fight condensation:
1) damp absorbing coatings
2) anti-mold products.
Damp absorbing products are water-proof and collect part of the water depositing on the wall. Such products also includes anti mold fungicide. Wykamol paint is one of the best products, even if a bit expensive: http://www.i-sells.co.uk/anti-condensation-paint-5.0ltr-%28wykanticon-wh-5%29?gclid=CNjEl6a_77sCFQjlwgodIgoAAQ
Anti-mold products prevent the depositing and proliferation of mold and mildew using fun. With our climate such products represent an effective way to fight the effects condensation and are cheaper than anti-condensation coating. Here a good wall coating product: http://www.diy.com/nav/decor/paint-woodcare/specialist-paints/anti_damp_paint/Ronseal-Anti-Mould-Paint-Silk-2-5L-11348504
Anti-fungal additives can also be added to different types of paint: http://www.i-sells.co.uk/anti-mould-additive-for-emulsion-gloss-paint-50-ml
Damp-resistant coating does not eliminate the moisture in excess from the internal environment, and it is only a partial solution to the problem.
Filling the walls' cavity with polystyrene improves the thermal insulation of the building, reducing the difference of temperature between wall's surfaces and internal atmosphere. Thermal insulation may help reducing condensation, but is not a complete solution to the problem. A moisture loaded environment is unhealthy, and improving the insulation of a single wall may result in vapor depositing on a different surface. The definitive solution is reducing the levels of moisture in the air.
If condensation occurs it means that there is too much water in the air. The problem usually happens because of insufficient ventilation. The best solution to condensation is increasing the room's ventilation. One or more passive vents can sensibly improve the situation. At the bottom of the page in this link are shown several examples of passive ventilation system: http://www.sovchem.co.uk/condensation-control.html .
If passive ventilation is not enough, then an active extractor like this: http://www.homeventilation.co.uk/cyclone.php can do the job.
Passive ventilation requires an opening in the wall. If this is not possible, then the only solution is using anti mold or anti condensation coating on the wall, minimizing the release of vapor inside the building and ventilating the rooms as much as possible.
My suggestion is to proceed with the cavity insulation.
Finding ways to improve the room's ventilation is essential. Make sure that room and affected space are ventilated on daily basis or when possible.
If ventilation and insulation can be sufficiently improved you can first try regular paint with anti mold additive .
If the problem persists use Wykamol or a similar anti condensation paint. The anti-mold paint is less effective.
The situation can also improve using a dehumidifier in the room. If there is condensation a small dehumidifier will not be enough. A 12l machine is ideal for most rooms. Here an example: http://www.screwfix.com/p/wdh-122h-12r-12ltr-dehumidifier/72503?kpid=72503&cm_mmc=Google-_-Product%20Listing%20Ads-_-Sales%20Tracking-_-sales%20tracking%20url&gclid=CNvghKPH77sCFULnwgodK08A4g
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