How tall and wide is this tree, and how wide is the garden?
I don't know whether solicitors' questionnaires to sellers include a question about knotweed. If they do, the seller may well be at fault for not declaring it (hard to miss a 6ft high invasive plant in your garden).
Dove, you're clearly a survivor too - I'll bet you have sticking up purple hair as well.
I've just been clearing out the garage and found a couple of those in a bag, Dove. I didn't think they went back as far as the 60s, but they're clearly survivors.
You should look at other people's gardens and open gardens such as National Trust and really analyse why things look good or not so good. My style is to echo what happens in the wild - for instance you don't see bluebells growing in a row.
I think he's trolling, jo47. We've got a troll at the bottom of our garden as well.
There is an issue with preserving the integrity of the damp course, which appears to be at the top of the white part of the wall on the left side (half way up the steps on the right).
Dig out as many nettles as you can, following the runners as far as possible, then next spring dig the new shoots out again, then later treat any further regrowth with glyphosate when it's got plenty of leaves.