They are mysterious because we've lived here for 12 years, never had any issues with damp, have a roof that is only 6 years old and have tiles, guttering, pointing etc. checked.
What else might be causing these patches? It's a south-facing, external wall of a 1906 house. The first patch appeared mid-January and although they fade in dry weather, they don't fade completely and they definitely get worse in the rain. If we'd not already had the roof etc. looked at by various people then I'd put it down to that but it's frustrating that we can't find the cause - it's DD2's bedroom and had been finished about 6 weeks before the damp patches appeared. The lining paper on that wall seems to be coming unstuck too so there's clearly something wrong.
I've attached a couple of pictures of the patches and one of the wall prior to decoration (is used to be the kitchen, hence the visible pipes).