How can I make sure that I own the copyright in website designs I produce for my client? At the moment, I have a contract, and it says nothing about copyright.
As (presumably) you are not an employee of your client, you will be the first owner of the copyright in your work product. Unless that ownership is expressly transferred to the client, it stays with you.
Notwithstanding the default legal position, it is common to find simple clauses in contracts making it clear that ownership in copyright works does not pass to the other party. For example:
Save to the extent provided otherwise in this Agreement, all Intellectual Property Rights in the Deliverables are and shall remain the exclusive property of the Designer.
If you use this example, you will need appropriate definitions of "Agreement", "Deliverables" and "Designer" - or better adapt this according to the definitions scheme in your existing document.
NB this does not deal with the question of licensing - what rights does the customer have to use the Deliverables?