Adding more thoughts. Things are changing fast. World ranking Universities are receiving unprecedented numbers of international applications. The numbers applying to Harvard verge on silly. At the same time London is becoming more international, and academic sixth forms even more so. It is no surprise that Whitgift is adding boarding, joining Westminster, SPS, and Dulwich as well as the more traditional boarding schools. There is huge demand from talented applicants for places at schools which will then offer a good platform for Oxbridge and Ivy applications.
This is leading to some oddities.
- British Universities normally have separate targets for home (including EU) and international students. For some very popular courses requirements for international students can be lower than for home students. I absolutely don't know, but would not be surprised if the "improving year on year" Oxbridge success of some big name schools hides a shift whereby their success with those categorised as international students is improving and this masks increasing problems achieving places for home students. My understanding is that only 30% of students at the LSE are EU. My guess is that numbers at Imperial will not be dissimilar.
- Contextualisation. Demand for popular, especially maths based courses, is huge and growing. If you are a very very bright European wanting to study engineering or economics, a three year degree with full access to loans and fee remissions at a British world ranked institution will be very appealing. These courses will be turning down a sizeable number of good students with three A*s or more. They will also want to recruit a higher proportion of students from "bog-standard comprehensives in the north".
Trouble is that entry requirements are now sky high, and the technical content of the course will reflect the ability of the students coming in, whilst there is a limited pool of strong mathematicians emerging from priority schools. This problem is exacerbated by the fee and loan system which means that less well off candidates from the north are more cost conscious and likely to prefer Liverpool or Newcastle to a more prestigious University in London. This is giving London a problem as the proportion within their British intake of both southern and privately educated students is growing, these figures are published and it simply does not look good. (In my day public school types went to Oxbridge or Bristol or Durham. Bright kids from the state system came to London which had the same standards but nothing like the same social prestige, and did not require you to stay on at school for an extra term.)
This may be some of the reason for the recent but marked shift towards British students without previous US connections applying to American colleges. If you can get into a top American college, perhaps more easily than an American based candidate might, but will need not just the same, but better results than your international classmates, and those applying from the state sector, it becomes appealing. Especially if your parents own a London home with bags of equity and a paid-off mortgage.
For Americans the reverse can be true. They had always assumed Earl Jr would follow father and grandfather to Yale but find that: he has his heart set on a specific subject, eg law, engineering or economics so is not interested in Liberal Arts; that he has a place at Cambridge whilst Yale no longer seems particularly impressed by family tradition; and that the degree is a three year course and only (!!) £18,000 a year, a massive saving.
Things will keep changing. The competition for popular courses is likely to continue to grow at a fast pace, and more English students will start looking to the US and increasingly Europe including especially Ireland grade requirements are higher but they don't contextualise them, giving English students from good private schools a much clearer run. As well as new degree courses taught in English in the Netherlands and elsewhere.
Sorry most of this is completely off topic. OP your daughter should go to the school she wants to go to, work hard and enjoy her education, finding time for some rewarding EC. It will have changed again when she is ready to apply.