Daogroupie is spot on. There is some difference of opinion about how much work you should make a child do if they are not willing, but if a child is keen and enjoys the challenge of the papers then there is no logical reason to prevent them! After all, the actual exams should be fun too - a challenge! - I know in this stressful age we forget it, but actually, I remember rather enjoying my entrance exam! And an English essay written by someone who is clearly enjoying themselves and relishing the experience will be a whole lot more fun for the examiner to read than one where the candidate has carefully rote-learnt lists of wow words, added requisite numbers of adverbs or fancy 'linking words' etc etc etc.
And an entertained examiner = a high mark.
One English examiner's secret tip - whilst officially no-one will ever mark a candidate down for having messy handwriting, with the best will in the world, if the person reading your child's answers has to struggle to make out every single word, it does interrupt the flow, and make it harder for the examiner to fully credit what the candidate has written. So if your child's handwriting is abominable - do get them a decent pen and try to get them to see legible handwriting as a necessity rather than an optional extra.