Wow that is a lot of questions, Piglet John! I shall try and answer them concisely if I can!
The DPC is not even all the way round the house. I suppose the plot slopes a tiny bit, enough for a small step in the back garden, and it is lower at the front than the back. I wouldn't have thought it was 9" above the ground there - more like one bricks worth.
I had wondered about the gutters. We had them cleaned about a month ago because one of the down pipes became disjointed so that was fixed and the rest of it cleaned. Funnily enough, although the broken downpipe caused mould in DS1's bedroom, the ground floor in that corner of the house isn't mouldy. Probably the only corner that isn't actually. The sides of the house, where there are no gutters are affected the worst though.
The neighbours have been having their gutters replaced in the last couple of years. I think we might need to do the same. The builder guy who cleared out the gutters said that they weren't fitted properly - they are lower in the middle than the ends so water in bad weather will pool there - I should think in the current weather conditions have tested this but the damp patches predate the bad weather. I started noticing most of them in the summer and some are much older than that.
The damp runs about 30cm up from the skirting boards round the rooms. There are places where it hasn't taken hold but it is spreading. It is in all the downstairs rooms except the little study but there is only about 6.5ft of exterior wall there. It is a very small room.
I don't know if the other neighbours have the same problem. I haven't really asked them.
Yes we have a water meter - I think it was fitted last year. And yes we have mould is in a room with a solid floor - they are all concrete. I noticed it first at the back of the kitchen cupboards a few years ago but didn't really do anything about it. I assumed that it was poor ventilation between the wall and the cupboard and maybe somebody had split a drink in there because that is where we keep that sort of thing. Also, we had had a leak under the floor which we never found which ruined one panel of our newly refitted kitchen on the other side of the room but strangely, everything apparently dried out. I suppose it could all stem back to that. I know water can take a long time to come out but would it be years?! 
Oh and mysteriously a whole new damp patch has appeared in the master bedroom in the last couple of weeks. I suspect that it is caused by the weather and an old and dodgy fascia board. There is a downpipe just there too. I don't suppose they are connected but who knows?
I think that about covers it. I reckon at the very least we need new guttering but could that be causing the problem all the way round the house?