Black mould is caused by condensation, which in turn has been caused by a humidity increase, the mould will usually appear first in areas that are coolest as the warm air cols and thus causes moisture (condensation) ventilation can help but does not always remove the moisture increase.
The best advice is : the existing mould requires a chemical treatment to kill any mould spore , then have passive humidity vents installed (look on the internet).
We do this sort of work almost everyday for social housing

Dont know whereabouts you are but we carry out a full inspection.

mould is caused by condensation. solution air brick ,heating,and ventilation fit extractor fan suitable for size of area it must remove so much millilitres of water/hr
all 3 must be done open windows install heating condensation is warm air on a cold surface rising damp rises only upto 1metre maximum as for damp metres load of balonie you will see rising damp above the skirting.

This sounds like typical condensation damp. the fact its only on two walls (i expect them to be external) says that the damp air is condensating on the colder walls in the room. there are a few ways to resolve this problem but all are based around air flow and temperature control. As substructure said fit an air brick to help air movement or there are fans that can be fitted to create artificial air flow within the house.Do you have filled (insulated) cavities in your external walls as this will help with thermal values. If the walls are external you can fit insulated plasterboards or insulated studwork internally to keep the thermal values up and stop the damp condensating on them, you can also fit a radiator in the damp area although the damp will still go to the coolest area of the room. There are also many products to remove the mould although if you dont deal with the core problem it will keep coming back.
For a full diagnosis i would need to see the problem but hope this is enough for you to work with.

mould is generally associated with condensation /ventilation probklems ,could be simply install airbrick/vent to area affected but without seeing im guessing

May i ask how the second guy tested the wall to determine its rising damp?
maybe used a Protimeter or similar device,it has two points on the end that are pushed into the skim plaster and in some cases the brick if its exposed!

As for the first one stating its Condesation as its "near the back door" hmm i dont understand his theory..
I agree about units,cupboard will cause moisture to be trapped and then resulting in mould growth.
Sounds like a possibility of poor ventilation and even though the " Condensation Period" is over as its from October to March,you can still cause moisture in the air from Cooking,Washing,Clothes on Radiators,Family living and even a Large dog.
Moisture has to go somewhere and if the home is poorly heated the damp will collect in cold spots so Ventilation is the key.Maybe if you do not have a Vent in the area concerned you could add one or a Heat Recovery Unit that takes the stale damp air out and brings the fresh air in and warms it.

Good luck.

Scott Cannon.

C&C Painting......Rising Damp can rise above 1 metre and as most trades believe its a no no....Look into it and either Google the BRE findings or PCA or even look at the history of rising damp and its causes/findings.

As for the Instruments used to detect Damp/Rising Damp why are these produced? maybe just so a Surveyor can look good!!!
As for just looking and saying hmmmm yes its damp because you have a sign of damp above the skirting! Really!!
I have been to properties that look dry with no salt/water marking and the meter goes straight into the red.
Also i have worked with CSRT Surveyors that have tested with a electrical Protimeter and it shows damp! Client is not so convinced so it has been tested in a Calibrated Speedy meter and found to have moisture content.

condensation but air brick in the wall .