If you are not already aware, the term Oxbridge refers to both Oxford and Cambridge, quite definitely the pinnacle of aspiration for university in Britain. This is for several reasons and, while you should be clear in your own mind which of these apply, it is quite clear to me that if you succeed in getting in (colloquial English), then to some extent you have a lifetime award that often simply opens doors that would otherwise be closed. Part of the reason for that is because a first degree from these two places is tackled in a different way from the process elsewhere; you are thrown into the deep end and must survive largely on your own resources. This element of self-reliance, directed at your study and motivation is why the degree matures to an MA after a suitable passage of time post-graduation. So you can have an MA in Engineering, probably two years after completion of your degree. You might also note that at Oxford a PhD is called a DPhil and in some quarters, calling it a PhD instead is an indicator of doubt as to your authenticity. For a long time you didn't have a certificate for Oxbridge degrees and the process at job applications was to point the employer / interviewer to the phone book and suggest they ring to check.
So, how do you get in? By being smarter than the average bear; by being the very best at your school; by demonstrating that, for you, school has not been difficult such that you have this string of academic awards and evidence that your capacity is quite a bit greater than school demanded. So while you hear of people offered places with 'just' three A-levels, if you look at the profile of students there and their academic record, say in UCAS points, you discover that the standard is a lot higher than the published offers suggest. ¹
Think you're good enough? Acceptance there is not simply are your grades good enough but whether the university thinks you'll survive (cope with, benefit from) the experience. I am not saying you can't get in with only three A-levels, but your competition for the place you want is doing four or five. Back in the Cambrian era when I was there things like county colours in sport were an expected adjunct, senior prefect-ship activity outside school, other qualifications – all evidence that you will cope with the extreme speed at which these two universities expect you to function.
Perhaps that establishes the academic standard; put simply, the very best.
As for an application, you will have been told by your teachers that they think you are a good prospect, which results in, one presumes, an impressive UCAS application and wonderful predicted and actual grades. Let's direct our attention to what happens if some interest is expressed. There will often be a critical thinking paper (go find these, they should be easy and your school may already have added a similar qualification to your portfolio). You might be given entrance papers—STEM papers ²—and can prepare accordingly. You can only apply to one of Oxford and Cambridge and you apply for a subject at a subset of the colleges within the university; thus you will be interviewed by a representative of the colleges to which you apply, which might be only one interview at one college. You will have an interview and that is what I look hard at next.
The interview has several objectives. Quite a few of these occur simply because the demand for places far exceeds the places available, so that the colleges can choose in a selective way. Their objectives include keeping their own results very high, trying to demonstrate inclusiveness (ethnicity, background, advantage) across the university and trying to keep their own college as high up the internal league table as they can. All of this means that the competition is fierce.In practice the interview has several objectives for you as an interviewee. We might assume that you academic prowess is shown to be extreme by the paper evidence, so the interview serves to explore what you can do with this. So, in general there is point at which you are asked about a topic and steadily stretched from what you know, to what you think you know and then (projecting beyond the available data) into what you think might occur, perhaps given some additional (new) information. This is quite difficult to practice without access to others of the same experience, but you might already be demonstrating the expected ability in the ways you investigate things you don't already know about. You're not there to score points, you're there to demonstrate that your thinking is fast enough and versatile enough to show that you will cope with the expectations of performance.
You can easily explore topics for this.³
When you look at a question, say "Why is the sky blue?", you will have, I hope, some replies that come instantly to mind, perhaps including "Why have I not asked this myself already?" Let's suppose that this is one you haven't asked of been told, so you might then come up with several possible answers, for example, that's the colour of the gases up there, or that the blue light is reflected back (okay, why? Why the blue not the red?), and so you can demonstrate that your thinking produces responses and rejects some possibilities). If you jump straight to 'scattering' because you've heard some of this before, what sorts of scattering do you know about? Why is the colour of the sky a different blue or even not blue at all in different places (on the planet or in different parts of the sky)? So you take what sounds like a very simple question and turn it into a demonstration of how you answer, how you use what you know (and don't know), how you modify answers/responses as you —without external prompting—bring other ideas to mind.
If your response to such a question is to (pretty immediately google it, then I'm sorry, you are not demonstrating attributes that the question serves to demonstrate. You would instead be demonstrating that you think the answer is the point of the question when it is how you go about forming an answer that is the point. If you don't follow that argument, you are telling yourself that you are not suitable material. Perhaps not now, perhaps not ever. This paragraph serves to point you to the frame of mind required to approach such questions.
I'm going to stop there. One of my objectives with this page is to help you decide that Oxbridge is or is not for you - just because many people say it is the best, that does not mean it is the best place for you. You are looking at you first taste of university, quite possibly your only taste of that, so it seems to me that you should apply yourself to where is best, but best for you, not for those around you. I covered this topic in the earlier pages, and one of my lasting lessons from running those courses in China was that many of the aspirants were going to university for reasons that attached to their parents family or school, not for reasons of their own. The cachet (and there are other applicable descriptors, such as pride) that a parent or school has in saying that they have a child/pupil at Oxbridge is sufficiently attractive that it does (visibly) affect what advice is given; too many advisors want the positive result for their own reasons, where good advice helps you make your mind up; it is your decision.
Just becasue Oxford and Cambrtidge take this approach does not mean that tehy are the only ones who do so. Nor does it mean that other universities require or expect the same approach. But you might see it as evidence of an enquiring mind and that this, the pusruit of learning, is what it is that the 'better' universities are looking for.
DJS 20201210
¹ But looking at The Complete University Guide, the average UCAS points for a new maths student at Oxford is 628 and for Oxford as a whole is 571. https://www.thestudentroom.co.uk/showthread.php?t=3448685 See if you can find the current statistic and the matching ones for Cambridge.
Me? I was the only person doing a 4th A-level, which I did on my own; I was deputy Head Boy at a state school of around 1100, which meant I was quite often the only prefect on duty at the Junior School (Y7-9, 500 or so), or the senior on duty on the other site; I earned county colours in Cross-Country every year from Y7-13; I did a lot of music; I ran or helped run many school societies, having founded some of these; I didn't do Duke of Edinburgh, because I was instead assessing it the last two summers of school. See what I mean?
² STEM = SEVENTH TERM ENTRY PAPER, implying that they follow after A-level results, from the days in which one often did a third year in the Sixth Form to polish your application and bridge the gap from A-level to entrance. These are available and historically so, so that you can explore and practice, recognising the breadth and depth that is expected. This is the sort of work you would do on your own, perhaps with a little support (discussion, in a collegiate style) with a capable member of staff, but you might well need to recognise that you are the one who is out front and ahead. This is not secondary teaching and if that is what you think is occurring you're having too much help.
³ Search Oxbridge interview questions, then again with your subject title added. This is not a list of stuff you should know, it is a list that shows you the sort of flexibility and adaptability that is expected. If you confuse the purpose here, you demonstrate that you are not suitable material.