How do I make sure that my work is protected by copyright?

In most countries copyright protection arises automatically. As long as a work falls within the remit of copyright protection, is original and is fixed in some way (e.g. written down or recorded), it is not necessary to register it. In the UK, there is no official register of copyright works. See UK IP Office guidance.

Since copyright is territorial, there may be still some advantages in registering copyright, for example to be able to file a lawsuit for infringement of your copyright in the US.

Even if there is no legal requirement to register it, It may still be good practice to add a copyright notice to your work; for example, 'Copyright [Author, Year]. All rights reserved'. While this is not necessary for legal protection, it does clarify the copyright status of the work for anyone who wishes to use it and indicates whom they should contact for permission.

Before you mark your work as your copyright, you should also consider:

Is the work protected by copyright in the first place? To be protected, a work must 'be original', in the sense that it is the 'author's own intellectual creation'.
Do you own the copyright? Check UCL's Intellectual Property policy, which outlines the general position for staff and students, as well as exceptions that may apply.
Are there any institutional or funder policies that require or recommend your work is licensed ans shared in a specific way? See for example UCL's Publications policy. Even when no policies apply, you may still wish to license your work in a way that allows others to reuse it as long as they credit you as the author. Check the Creative Commons website for more information.