Firstly Thanks to everyone. Secondly. I've been up and down stairs all day and am still no nearer finding the solution. I've logged what happened at each change and just hope one of you brainboxes can work out what needs to be done - I admit I'm lost! Please see the diagram (and find it in your heart to help - please!)
Paul
That's a really helpful and clear post - and I was looking forward to the challenge. But.....
I can reconcile all but diagram 2. I gather that this results in Landing sw. controlling lamp, regardless of position of stairs sw. This doesn't compute with me cos you haven't changed landing connections... and rewiring stairs sw. doesn't provide a "permanently on" position, which would be necessary to achieve the result you describe.
For normal 2-way to work, the feed to lamp [effectively] goes into common on one switch, and the live from mains into common on other switch. If Diag 2 is just as you say, then neither feed nor lamp can be connected to stairs sw.
Interestingly, your original and your diag.4 produce the same result - i.e. lamp on only when both switches in "on" position - hence two switches are in series.
Please can you confirm I'm understanding this correctly - and that wires in stairs sw. in diag 3 and 4 are as orig.
There's almost certainly one (or more) weirdly wired junction boxes hiding somewhere. And I would be tempted to test that each switch is working correctly by taking off the switch and checking with a meter (or low voltage bulb / battery) that each make / break is working ok.
May be someone else will be along shortly, but so far I'm stumped by apparently conflicting symptoms. Sorry...