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Thanks for all the interesting insights. We had thought of the toilet paper issues, and in fact did pull of some sheets of the one we regularly use and put it into a glass of water. Within less than a minute it had almost dissolved into much. So evidently the toilet paper is not to blame.
Girls and wipes, when I say I never saw any in the toilet no, obviously not, and yes they do flush. The point I was making was that the wipes they use are usually in the bedroom, not the bathroom and the bin is usually full of them, with a few knocking about, dropped on floor etc. From this, I guess that if they were going to dispose of them in the toilet I would not see any around at all. I have questioned all of them, and they are adamant they do not put this kind of thing in the toilet. Of course they could be lying to save themselves from embarrassment, but I didn't get that impression as I had stressed that it was important they told me the truth and they wouldn't get in trouble.
We did call the water company and they did come, as yes they are responsible for the 'lateral' drain which used to be a private drain, in as much as they are on our land. We think there are 4 to 6 houses on each section, although without going and lifting everyones cover can't be sure. They found that their drain was clear, and despite rodding ours still had a partial blockage that was making it run slowly. They were good enough to put their high pressure hose down and cleared everything that was left away. They didn't have to do that but one of the technicians told me that many of the drain clearing companies are cowboys and don't know what they're doing. They take your money but still leave uncleared drains.
So, we now have a completely clear drain, and have bought some caustic soda which we will put through all the pipes, and use periodically to hopefully keep things flowing. All the kids know they must put only 3 things down the toilet which I don't have to describe on here.
The suggestion of a blockage from further down that somehow got into our drain. There is for sure a house next door but one that certainly could have been a culprit, but how this got against the flow to ours goodness only knows. Ironically though our next door neighbour had a blockage a while ago, which they blamed on our next door but one in the other direction, but as we are first on the line it couldn't have been them. And as we are certain we never put this kind of thing down, not us either. Which must mean that their blockage was something that had gone against the flow!!
Even the water company could not explain, although they did say if there had been a lot of blockage in their drain which had gone all the way up the run, and then had been subsequently been cleared further down, some of it could have got into ours, and also next door's. The people who might have been guilty have moved away now so we can't ask them. We have told the new people, as they have a little child what has happened.
We may never know how this came to be, but we all agree that it doesn't do any harm to raise your drain cover periodically to check all is running freely. We take our water and sewerage services so much for granted and never give it a second thought until something like this happens.