In this sentence:
She is in Burford now, - little town near London.
Which article do we use? "a little town" or "the little town?"
"A little town near London" implies one of many little towns near London.
"The little town near London" implies one particular Burford that is near London as opposed to other Burfords around the country or the world.
In general, if there is no ambiguity, "a" would normally be used.
Correct: She is in Burford now, a little town near London.
She is in Burford now, a little town near London. (Perhaps one of many towns near London.)
She is in Burford now, the little town near London. (only one town near London,)