From King's College Office (H Perrot); "According to the King's College Register, Neal Ascherson gained a First in Part I and Part II History, in 1954 and 1955 respectively."
So no other tripos, no part III, no MPhil... what we have here folks is a double first. Still very impressive, but nothing outlandishly rare. He'll have got a 1st for Ia, Ib and II and declared it a triple first when writing one of the article that mentions it at the bottom. This is picked up by spartacus, then passes to wikipedia, then to all the little answers.com that steal from wikipedia. And then it becomes gospel truth. The reality however, is that in fact he got a double first. While you could make a case for calling a first in all three years a 'triple first' (will less validity in history which doesn't even have proper 1a exams), this would mean that roughly half of people who got double-firsts got 'triple firsts' (as a good number who got a first in two years probably got a first in all three).
Zinkin: Maybe a triple first, depending on your definition. Arguably not as it wasn't a continuous tripos (though by that reckoning we essentially rule out the possibility of triple firsts a priori).
Ascherson: Not a triple first. An 'ordinary, everyday' double first. The giveaway that it was fishy, aside from the claim itself, was the remark that went with it that he 'received' a triple-first. You don't 'receive' double firsts, they're unofficial. You might 'achieve' a double first, or attain 'double first class honours', but you aren't ever going to 'receive' them (disclaimer: unless I am mistaken).
Orr: No record of her existence that I can find, other than as a first year at Girton. The update was made by an anonymous cambridge address without comment. I'm putting money on it that this is just vandalism by someone wanthing a cheap laugh at the free encyclopedia's expense. I could be wrong, but for the record if I'm right that's pretty pathetic.