Most likely england during the wars of the roses (14th-15th century). Dorne on the other hand resembles Arabia (however I'm not sure). But if I had to choose, the main story in westeros (lannisters vs starks) is very closely based on the wars of the roses.

The idea of the battle between ruling families comes from "War of the Roses" as Martin has said in an interview but it was a general practice all over Europe.
I think the time period is not a fixed single one as Dorne for me resembles an Iberian Kingdom, like Castille for example or an Arabic one. If anything, King's Landing reminds me of Rome and the North I can't decide between Scandinavian Kingdoms and Russians.
The resembling of real Kingdoms come from different time frames.