I don't think that children with English as a second language are disadvantaged in these tests, because they are aware of it.
My dc are bilingual and my dd did the 11+ for a super selective after coming to the UK 5 years earlier with no English. She knew she had to do the test papers regularly to familiarise herself with the words and she did learn an awful lot in those months (and I did too tbh, I had never heard a few of those words).
At a guess, at her school roughly half the girls are bilingual, so it cannot be a disadvantage.
Similar scenario at my ds's school, at least half the boys are bilingual, lots of them Asian. They all did the English & maths test to get in.
Those that have been tutored for years to get in are struggling by year 9. Many have tutors from year 9 onwards, because anything less than an A for GCSE is a disappointment (to the parents).
I wonder if I'm too laid back about the whole thing occasionally. Especially after meeting other parents for information evenings etc.
I now wonder if one of my dc are at the school you are talking about. About 900 pupils taking the test for 120 places (roughly).