From what I've read, the U.S. certainly put great pressure on to scrub the project, and Mountbatten was indeed involved in ending it along with the P1154.
Whether it would have been any good or not is open to debate ( forever ) - if relying on low level laydown for conventional attacks, then as the Tornado proved, it wouldn't have passed muster in WW2 - seems it took a lot for some people to realise jamming systems don't save one from a lot of lead thrown in the air above a target.
If it was purely to deliver nuclear bombs, the sub / ICBM had already come up with a system much more likely to succeed.
I agree re. the looks, slab sided & dubious looking wings - what was it like at medium / high level ?
I always understood the Jaguar inherited some aspects of the TSR2, notably the gear, empennage etc - look & compare the two.
As for the P1154 someone mentioned, and 'we might have had that too', I've always thought that was over ambitous even before the bickering service requirements knobbled it, and we had a lucky escape, going instead for what was to become the much more viable Harrier ( the Harrier GR1 received the INS & HUD intended for P1154 ).
If you want to talk about missed VSTOL opportunities see the late 1980's Kingston P1216 projects - various versions offered, my favourite was a twin tailboom type with an F-35 style nozzle between, and shutters forward rather than nozzles, to avoid drag.
There was even a forward swept wing version, using carbon fibre manufactured in such a way that the wingtips CONVERGED under aerodynamic load - now THAT is what we should have instead of the JSF !
There was a full scale mock-up at Kingston, which the prime minister of the day was shown around and promptly rejected the project - Margaret Thatcher...