Why not prep for another school from WHS?
Last summer, WHS got 50% A star and A grades at A level.
Westminster got 78% A star and A grades.
Your plan may backfire. She may wobble under all the extra stress. She may end up at a less good school than WHS.
I'm honestly surprised at this post. If you feel like she's not doing enough, get a tutor at home but don't risk your place at such a good school.
Also, A-levels and education can only take you so far. Applications far exceed places at the likes of Oxbridge. She'd be better off pursuing a hobby or extra curricula stuff and becoming truly excellent at it and standing out from the crowd in some other way than just sheer push push push educationally.
And even after Oxbridge it's not just the name of the place, it's the soft skills, the creativity, can you work with other people, can you lead, can you go the extra mile, can be you be humble, that get you a job afterwards.
DD is at WHS in top year now and it's in my view A LOT of work and there are many extra curricula things to keep you very very busy too that are fulfilling in a much broader way than just education that are great for putting on UCAS form.
At the end of Year 6 there's a small flight to Tiffin Girls at WHS some years. If you want more of a push, maybe go there. They got 72% A star and A grades this summer. It's a long way from the station though and a very different kind of environment.
Or you can jump to Kings sixth form. They got 87% A star and A this summer. Your bright child will do well anywhere. They really don't need to jump through thousands of hoops.