HI,
Damp can occur for many reasons and correct diagnosis is the first step to solving the problem.
On the face of it, It appears your damp is caused by 'free moisture' from the leaking guttering.
A leaking gutter can cause water ingress and should be attended to immediately to avoid the many inherent problems caused by damp such as decor deterioration, mold (associated health problems), wall tie failure (cavity walls) and loss of heat etc.
A complete fix of the cause of the problem is necessary as the first thing to do.
If mold spores are present treat them with an anti-fungal wash to fully eradicate the problem.
Another problem that can occur is hygroscopic salts or 'salt damp', in this case the problem area will need to be removed with a suitable physical barrier installed along with correct salt inhibiting preparation and finishing coats. In this case black mold will not be present but a flaking and bubbling of paint, wall paper coming away and tide marks are tell tale signs.
Salts may be present and will attract moisture even if the initial problem is solved.
In any case, you could wait to see if it dries out it should take a few days, also carry out a test the guttering for leaks with a hose to save waiting for a rainy day.
If it isn't drying out it should be apparent. At this stage correct diagnosis may be necessary to ascertain the correct solution.
Third party insurance backed guarantee are offered for this type of work.
Hope this information helps...
Best regards,
James.