GRRM took the War of the Roses as inspiration but there is not an exact one-to-one match between history and fiction. The story in the chronicles of "A Song of Ice and Fire" gives a longer history of a larger place roughly analogous to here-and-now England.
Martin draws some inspiration from historical persons for his characters and events but there is not an exact progression. One can see that the "First Men" are roughly equivalent to the historical Celts. The Andals with their seven kingdoms are roughly equivalent to the historical Saxons and the seven kingdoms they established in England (Kent, Mercia etc...), and the Targaryens are roughly the Normans. This is where the historical trends end their one-to-one mappings.
The direct historical parallels that can be clearly seen are:
GRRM also drew inspiration from other events in history. For instance he has stated the that the "Black Dinner", which happened before the War of the Roses in Scotland, was his inspiration for the "Red Wedding".
Casting Tywin Lannister as Richard Neville and Cersei Lannister as Margret of Anjou places father and daughter from fiction in two different families from history, indeed on two different sides of the conflict.
The book series, in short, captures the spirit of history but is not a one-to-one allegory.