A national sample is only necessary because different areas experienced different trends. Otherwise, you could just pick a small regional sample and extrapolate from that. The discussion was about the 80s and 90s recessions compared to today, not London versus the rest of the country.
I think our disagreement stems from something different. You seem to believe that house valuations exist, separate from any one house, the owner, and the buyer. I don't. I believe that house valuations for an individual house can only be determined at the point that house actually sells. In between times, no-one has any idea. I may have been in negative equity many, many times since I bought my home ... but I'd never know. You might believe that some index is a pretty good predictor of what a sale might achieve, but until you actually sell it you'll never really know how accurate it truly was ... and chances are, it won't have been all that accurate anyway. I might believe that Mystic Meg is a better predictor of what a sale might actually achieve, but unless it sells, I'll never know either.
What I do know is that the number of people who actually sold for less than they paid is a tiny, tiny fraction of the total sales. That is true going back 30 or so years, in all parts of the country. The data is publicly available, and the dataset is huge - so it is valid and reliable.
My contention - the thing I can't prove - is that where people did sell for less (and I accept that there may indeed be hundreds, perhaps even thousands of cases of this), there will be a story behind that that has more to do with specific circumstances at that time, for that house, for that seller than it does with the housing market in general. I can't prove that - but it's a narrative that I think the evidence that is available supports.
Oh .. and those charts showing flats in the North-East still selling for less in 2021 than in 2007 ... yes, the line shows the average price for flats hovering at £120k, dropping to £115k. That's a 4% drop ... over more than a decade. There's likely to have been just as much influence due to stamp duty changes, or different mortgage products available to buyers at the time as it was to differing negotiating positions and circumstances affecting sellers. If it was the reverse, I wouldn't call it a rise either, I'd call it a flat line. So technically, you're not wrong ... but I think you're stretching a bit far to say this is evidence of negative equity. Remember - I'm responding to @UniversalAunt stating that "negative equity would be an everyday fact of life for many & keys posted through bank/building society letter boxes". I don't think any of the people with £5k negative equity you've identified are contemplating that future - which your data on repossessions also supports. So we agree,sort of, right?