I am not in the UK, so can only talk about bilingualism in general terms.
Children can pick up superficial fluency in a language relatively quickly. However, being able to (say) function in a playground game, is not the same as being able to, say, describe how an electronic circuit works, or be able to talk about a book they are reading and give a verbal description of what it is about and what they like about it. And that is even before you get to the literacy side of things--being able to read and write at the same level as everyone else.
If a child of school age is exposed to a completely new language, it will typically take a couple of years for them to be 100% up to speed---and then, typically, another couple of years after that to catch up with the academic side of things fully. That's for a typical language. For Japanese (the language which children have to master here), it is actually even longer, because our writing system is extremely difficult.
In school, a typical task might be, let's say, reading a passage about how the water cycle works and then answering questions about the passage, using full sentences. To do this task, a child will need to have a decent level of vocabulary, including all sorts of words that are not used in everyday conversation with other kids, meaning that they are not just going to magically "pick up" this stuff from playing with other children and so on. They also need to learn English's complicated spelling system in order to read, and they need sufficient practice to enable them to read easily and at speed; if you are having to slowly sound out each word, it becomes hard to make sense of the meaning of what you are saying. You then need to activate all of this (spelling, vocabulary) in order to do written work correctly in English.
All of the above is describing the kind of situation where a child comes to the UK at a later age and needs to learn English from scratch.
If a child has grown up in the UK and gone to playgroups and so on, then it is a bit different; they will obviously be fluent in spoken English before they get to school. That said, if a child is not hearing English at home, they can sometimes have gaps with vocabulary. This is where the school system becomes really important. A good school system which focuses on building up a strong vocabulary for all children is invaluable for those who do not speak English at home.
England, Scotland and Wales are very unusual internationally, in that children who speak another language at home do about as well as those who speak English at home, which suggests that their education systems are doing a very good job in general; in most countries, children who speak other languages at home tend to be at a significant educational disadvantage.