OK,
From the employer's "side of the fence", I'm actually a big fan of these drafting exercises. They force a candidate to think clearly and express themselves succinctly under pressure - which is exactly what you're going to be required to do when you start work.
Don't assume that the drafting exercise will be law based (unless the firm has told you otherwise). There may well be non-law grads attending the assessment centre and so it is unlikely that you'll be required to draw on your existing knowledge of the law. If it is law-related, then it is more likely that the legal issues will be fictional (i.e. you're given a made-up piece of legislation or cases).
The alternative is that you're asked to draft something completely non-legal (as opposed to "illegal"!). I remember attending an assessment day at, I think, Ashurst Morris Crisp (as they used to be!) about 9 or 10 years ago and we all had to draft the rules to a well-known simple board game (eg snakes & ladders, draughts etc) but without using a diagram. You'd be surprised how difficult it is!
If you are given a "straight" legal problem to advise on, then keep reference to statute and case law to an absolute minimum. That's what you'll be required to do when you start to practise. You are NOT being tested on your legal knowledge (that's what exams are for), rather you are being tested on your ability to convey concepts, ideas and advice in a way which is easy to understand. For example, if the scenario involves a client's property being damaged by something on his neighbour's land then you're better off saying "Under English law, your neighbour is strictly liable for the damage which has been caused to your property - in other words, it won't be necessary to prove that he has been negligent". Rather than "The case of Rylands v fletcher in 1868 held that...." etc etc.
As with any drafting, you're trying to explain something as clearly as possible as simply as possible. Short sentences are good. A letter might start with a short summary of your understanding of the facts, continue to identify the main legal issues and then provide your advice. Sub-headings are useful - anything to help the reader follow what you're trying to say.
Right, for all my spouting about clarity and conciseness, I've rambled for ages.
Hope that helps....
Chalks.