If you hold a JAA licence, you don't need to do anything.
Your JAA licence will continue to be valid until it's expiration date; when you need to renew the licence (enclosing the usual cheque), the CAA will send you an EASA licence. The main difference being that the EASA licence will be valid for life & will not expire.
It is only those of us with a CAA (pre-JAR) licence or NPPL who may need to convert our licences.
CAA info