Looking for a full boarding school for sixth form

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Hi
I know virtually nothing about boarding schools so asking for advice. Husband had been offered a job in the Middle East and so we are potentially looking for a boarding school for my dd who will start sixth form in 2025. Would be good to be in reach of Heathrow or Gatwick.
She's pretty academic, wants to study STEM, but not particularly sporty or into drama. Need full boarding and good pastoral care. Co-Ed or all-girls both considered. I've had a look around and seems we are already quite late in looking so I'm panicking a bit!
Help!

Rugby School has great pastoral care and caters well for non-sporty types too. Being a full boarding school students do not disappear on the weekends as happens at many other boarding schools leaving just the overseas students at school. Rugby offers a full co-curricular programme which is especially important at weekends. There are other UK teens at the school with parents living in the middle east. Train directly into London Euston so easy to get to the airport.

Technically your application would be late for September 2024 but there are some great options that I think would still be available - Bromsgrove often has late places and has the most terrific pastoral support - it’s a really happy place and great for a newbie settling in !

Thank you @FencingForearmed , I am considering all these things! I think a full boarding school may be too much and she would prefer the option of quieter weekends but I think we'll go visit a couple of different options so she can at least get a feel. I've signed up for a few open days, trying to see a variation of options. Luckily we seem to have some time as applications are mostly in the autumn.