I don't know anything about those particular schools, but as a parent of bilingual kids, it is a fact that not speaking the school's language at home, or even speaking the school language BUT having parents who are not native speakers of the school language, can have a knockon effect on language attainment at the higher levels (which is what you are getting into at GCSE level).
It won't stop the girls being perfectly fluent speakers of English. But they may not be getting the full range and depth of idiomatic English and cultural references that you will be getting if you have an educated native English speaking parent at home. I'm thinking of a couple of friends I have from South Asian backgrounds. They come from prosperous middle class backgrounds and are well educated, but they sometimes don't "get" certain cultural references, British historical "stuff," references to rural British things, or certain idioms/turns of expression when they come up in conversation.
We are in Japan and my daughters speak both languages at home - my husband is a native speaker of Japanese. I have friends where they are their spouse are both foreigners and both speak English (or English plus another language such as Russian), while sending their kids to Japanese school. Of course the kids are fluent in Japanese. But the lack of home input can create gaps as kids get older which then lead to somewhat weaker performance in kokugo (Japanese language and literacy, as studied in the Japanese school system). It's a very good idea for parents to be aware of this and think of ways of supplementing the kids' vocabulary and cultural references in the "school language" (Japanese where I am, and English in the UK).
So it's entirely plausible that performance in the language arts may be a little bit lower in a school in the UK where many kids, even highly educated ones, speak another language at home most of the time, or are speaking English but with a parent who did not grow up in the UK. We are talking in relative terms, however, and I have no doubt that the girls in question are still doing extremely well in English by any reasonable person's standards, as well as in their other subjects. All the schools referred to in this thread will be very good schools, so personally I'd focus on where my daughter was likely to thrive and enjoy her school life.