@ACUNI123, I would never argue that LSE and Imperial are at the level of Oxbridge.
Apart from that, your post is quite decent.
@raincat, if you read my posts in this thread you might get a big picture of UK universities and their respective competitiveness:
If she is not one of those who has thrived during the pandemic, then I would suggest she skips and avoids attending Oxford, Cambridge and Imperial because studying is intense (i.e. pressure cooker environment) at those schools and they are shaped for certain types of motivated nerds, which she obviously is not.
There are other prestigious UK schools she can attend though and move at her own determined pace.
It also appears there is no clarity yet on the degree she wants, all you have indicated is that she is strong in Maths.
Here is a link to another post of mine that highlights the most prestigious UK universities for studying Maths and also for some other degrees:
Hopefully these links helps give a comprehensive insight in regards to UK universities.