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I live in a ground floor Warner as well, and I have damp in a similar area. Rising damp is incredibly rare despite what surveyors tell you. It's most likely penetrating damp from leaky guttering and/or the wind blowing the rain into the porch area (this happens to me, very annoying!), potentially coupled with condensation due to poor air circulation too.
A few Qs: Do you know if your air bricks are blocked? What kind of windows do you have? How do you dry your clothes in the winter? Are the fireplaces blocked up?
Area highlighted green is where the damp is. It's about a meter high at the front, tapering down to a point.
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