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Our place in SE23 has a side access which was registered in the names of some untraceable people with an address in North London. They were possibly the successors to the owner of the land when the area was developed in the late 19th and early 20th century. It was one of many such alleys in the area which would have been used for delivering coal, but most have been blocked off by people extending their gardens. We accepted the uncertainty on the basis that there was probably sufficient history of use for us to rely on. I ended up doing most of the bramble control. But yes, see what the solicitor comes up with, and be ready to accept some uncertainty.
Our current place has an even worse issue - our title stops at the threshold of our front door and “our” front yard is unregistered.
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