Many universities will accept application right until the course starts as they perceived Masters courses as cash cows more than anything else. There is no set deadline, although popular well-regarded universities will fill up more quickly.
Generally anthropology is funded by the ESRC, their deadlines are the first week of May, although you will need to have a place before you apply, and your university will probably want to assist you with the application. So, you'd need to start asap.