Unlike most taught courses, PhD opportunities are available all year round (although there probably are many that start Sept/Oct time). Apart from findaphd.com, good places to search for studentships are in relevant publications, such as New Scientist and on the website www.jobs.ac.uk
Also, check individual institution websites.
As you have recently graduated, why not have a chat with your tutors and see if they know of suitable research groups that you could approach prospectively? Good luck.