I think it must depend on a range of factors, though I have no useful experience (dd starts primary next year). All our local schools have over 50% children speaking EAL, and some up to 90%. I recently visited one, and thought it a lovely school. The headmaster, who was showing me round, raised the issue unprompted. He said, 'even though over 60% of our children speak EAL, in the main they come from families that are very supportive of education, and that means we can achieve impressive results - social as well as academic". The children were very mixed, with no one ethnic or linguistic group dominating (which would worry me - if 80% of the children share a language that my dd can't speak, that may be very isolating). They seemed happy and enthusiastic and well-behaved.
In another I visited, there were definite signs that it may be more problematic. For a start, they were completely astonished I wanted to visit the school - it was like no parent had ever visited before. And though I liked the school in many ways, and was really impressed by the reception teacher, I was really struck by the scale of the difficulties they deal with. Like: 20% of the children recent refugees, many from very traumatic backgrounds; 90% boys in some classes; 40% turnover in every school year. The alarm bells ringing for me are: within the classroom, dd could be the one child who doesn't need additional support, so could end up getting very little attention. In the playground, she could end up being one of very few girls, and maybe end up excluded linguistically from that small group. And, above all, she will have no stable cohort of friends to go through school with.
These things DO matter, but it's about getting to know the school and seeing what happens in practice, not making too many assumptions (e.g. EAL = bad school). If my dd ends up only getting a place at the second school, I will give it a go, but I'm really hoping she ends up having the benefit of attending a socially mixed school in a multicultural city without having to sacrifice her own learning or social life.