What's the Name of That Book??? discussion

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The Prime Minister's Brain
SOLVED: Children's/YA
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One child goes into a city tower for training/prize - others follow up rubbish chute! [s]
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Here are the details I remember:
There are a group of children, one of whom has been selected from a special competition, and has to attend a training session/ collect a prize. The children make their way to the location specified, accompanying the chosen one, and the location turns out to be a tall and ominous looking tower in the middle of several large motorways. They realise this is why the tower is called "_ island", and talk about how deceptive the name is (since it suggests an abundance of nature and water).
There is a semi circular, small, revolving door that takes the chosen child into the tower. The others get uneasy and decide to follow up a chute they find at the base of the building.
The chute has various openings, and on their journey up the tower they see a robot operated warehouse, and memorably a robot operated kitchen preparing meals. A robot dumps a bunch of potato peelings into the chute, right on top of the children's heads, causing them much discomfort. However, they remain determined to rescue their friend.
At some point we cut away to the chosen child, who is sitting in a clean, clinical classroom with very expensive computers, with many other children. The child later eats meals (the ones the friends saw being prepared) in a kind of canteen.
I think it is revealed that the whole scheme is orchestrated by an evil mastermind, who arrives on scene in a helicopter, but the group of children set fire to the building, ending this plan for domination.
I've forgotten what this book is called and it is really annoying. I associate it as being similar in spirit to the Gillian Cross books about the Demon Headmaster. Please say if you recognise the plot! It might not be 100% accurate but it's what I remember.