Hiya Em,
Best thing to do is invest some time in talking to the council contacts and if you can, visit the sites and ask around.
Sites can be run by the parish & private groups as well as the council so you may here of other sites and the people on the plots should be able to give you some intelligence about getting to chat in person with the person who runs the site /allocates plots.
There seems to be a lot of variations on policy as they're usually set locally. If there are lots of plots free it should be easy to get one if you don't live locally & if there are few available, preference is usually given to people living locally, but there are always exceptions.
My advice is to talk to the allotments secretary in person if possible & build a relationship with them, so they know you are keen and serious about moving to the area.
I popped in regularly & used to chat to the secretary & although I'm still on the waiting list for a full plot ( not quite at the top) , I've got a temp share of a chap's plot until he retires and has time to do both of his. Came about by showing interest & being more than a name on a list.
Good luck.