No. You can do your Licence now, and membership when it's due.
However, it's easiest to synchronise them. We have 4 memberships, each person with a different renewal date. I called the very helpful people in Manchester, paid a bit extra - pro rata rate - and got the renewal dates moved to 31st December each year.
Mind you January is expensive now, with tennis club, cycling club and BC memberships all hitting at once.