When someone creates original literary, dramatic, musical and artistic work, (including illustration and photography) they automatically inherit the rights to that work under the Copyright, Designs and Patents Act. This was designed to stop people from taking your work and using it as their own.
A Trademark however, covers other types of intellectual property, such as titles, names, short phrases, and slogans; familiar symbols or designs; or mere variations of typographic ornamentation, lettering, or colouring. These things are not protected by Copyright. If you think your work needs a trademark, you can apply for one here.
When creating designs, you are allowed to centre around a theme. What this means is that contrary to popular belief you are allowed to create designs based on things like tv shows and films. What you're not allowed to do is rip off their work. We recommend achieving this by using your own artwork and checking the government database (link at the bottom) for specific trademarks. Parodies and fan art is usually acceptable however there is no solid line between what is ok and what isn't, you just have to take issues as they come.
An example of a design centred around a theme but not in breach of copyright.
This is both fan art and a parody, the designer used all their own original artwork and typography.
We also strongly suggest that you have a specific ‘contact us’ page (called a 'DMCA' page) where you can receive complaints from anyone that owns the rights to take down the content, whether it may be a Copyright, Trademark or otherwise. We have a page of our own here that you can use as an example here. DMCA (or digital millennium copyright act) complaints are by far the best way of resolving copyright issues. Companies will almost always check for a DMCA page before filing an official complaint. This give them a chance to let you know you've breached copyright before they have to chase it up. When a DMCA complaint is made you can simply remove the infringing content and carry on.