Speaking from recent experience of very selective but not as selective as Westminster and St Paul's, London schools, I would say the pupils increasingly see Oxbridge as a lottery and therefore do focus their sights on other top universities, and the USA. The numbers applying to US universities, especially the sporty who are courted for scholarships, rose considerably in the last five years.
The admissions process has always thrown up surprises but year after year they see the brightest not getting in, and some strange choices who do (though that may be related to courses, college etc. as much as the idiosyncrasies of the process). So a culture of seeing Oxbridge as a punt has grown up and the schools are finding it harder to persuade pupils to apply, why put yourself through the stress and extra work, when if, with A* predictions, offers for other very good universities are going to just land on your mat (though probably in April if it is Durham
). Especially if the Oxbridge ethos doesn't appeal, and it isn't for everyone. Or alternatively you may have the exciting prospect of going to the U.S. and the attractive choices of generalist courses there. In DDs year, who left last year, very few of the brightest even applied, and numbers getting in were down again. There is also an increasing tendancy to focus on STEM subjects and more vocational courses such as Engineering and Law and those of course are the most competitive, as well as there being very good courses other than Oxbridge.
That is a good thing though, isn't it? In terms of widening access. You do only want the most determined to apply, and to take up that automatic path from very selective indies to Oxbridge. The pupils don't really have a problem with it, they get great experiences in London and other good universities / the U.S.. It is just the Oxbridge focused parents like OP that struggle with a changed environment.