This clause is about competition - not a competition with prizes, though.
The Author shall not during the continuance of this Agreement without the prior consent of the Publishers in writing publish any abridgement, expansion or part of the Work in serial or book form, nor shall the Author prepare other than for the Publishers any Work which shall be an expansion or abridgement of the Work or of a nature which may reasonably be construed by the Publishers as likely to affect prejudicially the sales of the Work which is the subject of this Agreement.
This is sometimes called a 'competitive works' clause. It means you can't slightly adapt your book and publish it with anyone else, and you can't write a very similar book and publish it with someone else. You might think that this doesn't matter as you wouldn't want to anyway, but the key phrase here is 'during the continuance of this Agreement'. This should be backed up by a clause somewhere that says rights will revert to you if the book goes out of print for longer than a specified period or is withdrawn and not reissued. You should be able to publish a version or adaptation of the book if the publisher is no longer selling it, so you need to make sure that the agreement will no longer be in force in that case.
This is a reasonable competitive works clause. It relates to a work of fiction, and to be honest I'm not likely to want to rework the book. Once a book is published, I forget it and move on. But what if you feel you didn't do the book as well as you would have liked, you've sold it to a tiny publisher that is going to achieve only very small sales, and you wish you hadn't? Well, tough. You will have to wait until the agreement has come to an end before you can go back to that book, unless you ask for the publishers' permission - 'without the prior consent of the Publisher', it says. The publisher may give permission if they have no plans to reprint the book and it is not doing well. But they don't have to, and they may see no reason why they should. So for the competitive works clause to be acceptable you need to look at the whole of the rest of the contract to see when the agreement might be terminated. Now that print-on-demand means that a book need never go out of print, the old-style termination clauses do not work very well. We will look at termination clauses another day, but remember that the competing works clause and the termination clause go hand in hand.
In a contract for a non-fiction work, you may see a much more restrictive competitive works clause. The publisher might try to get you to agree not to write a book on the same topic for the same market, for example, or not to write any competing works. Now this clearly isn't viable, as you will very quickly have signed away your rights to write any more books on the topics you know about.
If you are writing a book about dinosaurs, and they want you to promise not to write more books about dinosaurs for children, you will have to argue about the clause. The chances are, they are paying no more than £2000 to write a book about dinosaurs. How can they expect to buy up your whole career for £2000? Of course they can't, it's unreasonable. As soon as you point this out, most publishers agree to change the clause. They probably won't get rid of it completely, but you should have the chance to re-word it so that you are happy with it. Be much more precise about what constitutes a competing work and in what time frame the work must be published to count as competition. You may promise not to write another 24-page trade pop-up book about dinosaurs for readers of 6-8 within three years of publication, for instance. And if you really feel the need to do one, you can always publish it under a different name.
If the publisher is adamant that a very restrictive competing works clause has to stand, walk away from the contract - unless they are either giving you a very good deal, or you are absolutely certain that you won't want to write more on that topic. If it gets to the point where you are about to withdraw from the deal, they may well back down. But don't do it to call their bluff - if you have said you will pull out if they don't change the clause, you have to do so. Before you get to that point, though, you can point out that the clause is a restraint of trade and so technically illegal. They are allowed to impose only 'reasonable' restrictions on you, and they have no legal right to be free of competition. Of course, 'reasonable' is open to interpretation.
The less common clause that requires you to offer your next book to the same publisher is also a restraint on trade, so you don't have to accept that either. We won't come across that clause in the contract I'm using as all my publishers already know I'm not going to accept that one so they don't include it any more. If you find yourself agreeing to such a clause and then regret it, make sure you offer them a book they won't want to publish. So if you are writing picture books, offer a book on customising your car or losing weight by paragliding. Best to check they don't have a list such a book would fit into first, though. On reflection, it's safer to get the clause removed in the first place.