Well as I'm sure you know, the "make it British" business is all to do with politics, on the basis that a purchase can be presented to the public as being somehow more acceptable if a significant proportion of the aircraft is British. Of course it's absolute folly, as the purchases would be either less expensive or more practical if they were simply "off the shelf" from the US... but try convincing a politician of that!
The Phantom was one of the best examples of how stupid the concept is. A waste of money putting British engines into an aircraft which performed just as well (better in some respects) with the standard US engines.
The poor old TSR2 was just unfortunate to come along at precisely the wrong time when the Government was running out of money, and thought that they could bully the various aerospace companies into merging, in the hope of saving cash. The result was that an aircraft which could have been easily produced by English Electric, became the victim of a never-ending series of committee decisions and inter-company squabbles, primarly because Vickers evidently thought that the project was essentially theirs - or at least that it should be. When you add that situation to the unavoidable cost of developing such a complex aircraft, the difficulty of relying on completely new and untried engines, and pressure from America to buy their product, then the aircraft was under attack from all angles and it's hardly surprising that it got chopped.
There's no real mystery to the saga at all - it was just a classic case of gross mismanagement. The notion that there was some dark motive behind the hasty destruction of the TSR2 jigs and surviving airframes doesn't bear scrutiny either. Obviously, once a project is abandoned, then everything associated with the aircraft is dumped. It seems entirely reasonable that Warton and Weybridge would clear everything away when they had other projects which needed the space (for example, Warton had to shift some parts of the Lightning programme in order to make space for TSR2). Likewise, the notion of using the two flyable TSR2's on test duties was considered and it was only the cost of doing it which seems to have discouraged the Government from going ahead. It's easy to say that there was some dark plot to destroy everything either to keep America happy or to spitefully ensure that an incoming Tory government couldn't resurrect the project but in reality, America probably didn't care about TSR2 that much, and no incoming government would have seriously considered re-starting the programme in any case.
Ultimately, the TSR2 saga has suffered from the "Elvis Presley Syndrome" with all kinds of myths being attached to it because it was cut-short at just the moment when it started to show some promise. It's easy to speculate on what might have been when there's no chance of ever finding-out! Being dead is always a great career move!