OP, I understand where you are coming from. My DC are at the end of the process, and have enjoyed their London education. However both are pretty robust in different ways, and have been aware of "anxious" children and the heavy pressure placed on some. I don't know what schools Seriously has experience of, but I suspect things won't be much easier in what might be considered "less academic" London schools.
London has lots of different tribes, but two that can cause disruption are those that are absolutely focussed on a good US school. Entrance involves endless box ticking including evidence of "leadership" and broad high level extra-curricular. So lots of tutoring outside school, lobbying for posiitons such as sports captain, a need to maintain "class placement", lots of fretting about achieving straight A*s and whether individual teachers are good enough to deliver (some of the parental bullying of teachers we have witnessed has been quite shocking), and so on. Then the international rich. I can think of one child who seemed to be being raised by the bodyguard as the mother spent as much time as possible in Paris, and the dad was busy "exporting to Africa". DC have some great "children of oligarchs" anecdotes. There are some pretty fundemental culture clashes between children from very priviledged backgrounds and traditional British school set ups. Anecdote has it that one or two Headteachers are blinded by the bling and don't stand their ground as well as they might.
Looking back I am convinced that it is the "right school for the child", not the school that performs best in league tables. And that a wider ability intake, as long as the bright kids are getting the results they should, is often a good thing. Having like minded and supportive peers is very important. By later teens peers have a much greater influence than parents, and if your DD has a constructive, emotionally intelligent firendship group with high but realistic aspirations, the whole sixth form/public exam/UCAS thing gets driven by them with no need for parental nagging. Its finding the school (state or private, day or boarding) with the right peer group.
I know quite a number, of particuarly girls, who have shifted school in secondary years for similar reasons. Boys in contrast seem to move because they are naughty or disengaged. Perhaps different responses to the same issues.
I understand (good source!) that Mayfield is experiencing a significant increase in enquiries from London parents interested in a school that enables girls to have a more normal childhood away from the pressures of London day schools. I assume the same is true for other smaller name but sound schools. Mayfield's advantage is that first St Mary's Ascot will syphon off the more socially orientated Catholics, and then that Catholic traditions tend towards inclusion rather than selection.