@singingstones I think this is such an important question - what makes Oxbridge suited to your child, or not? Here are my thoughts, for what they are worth. As someone said above, the workload is brutal, and the pace is relentless.
My sense was that if someone has had to work really really hard to get straight 9s and 4 A stars etc etc, then they might actually find the pace too much, because they didn't have much "left to give", if you see what I mean. Whereas, if they had achieve those 9s and A stars without actually having to work particularly hard, then they still have the capacity to go up a gear when they reach Oxbridge.
This was certainly the case for my son. He is naturally on the lazy end of the spectrum(!), but was lucky enough throughout school and college to find things easy and breezed through with very good results. He arrived at C (NatSci) and it was a huge change for him, but he could still go up that gear when he needed to. The first year was a big adjustment for him and he failed a mock exam mid way through the year. (He had never failed anything in his life before, so this came as a bit of a shock!) He knuckled down and we realised that he can work hard, it was just that he had never needed to before. And there is no doubt he has thrived and is absolutely loving his time there.
So, in addition to natural flair, curiosity and love for a subject, I do think having some "spare capacity" is important. I hear of kids who work all hours that god gives them for their A levels, and because they want to get in to Oxbridge, and I really wonder how they will cope when they arrive. As @HewasH2O said earlier: "Please don't think that getting an offer is the goal. The next 3 or 4 years will be far harder than at most other universities."... So true!
Hope this is helpful!