Large numbers of Westerosi Houses trace their ancestry all the way back to the First Men, in a more-or-less direct line. Is this similar to medieval England (so, in other words, English noble houses tracing their ancestry all the way back to the pre-Saxon times)?

Well, there are very, very, very few English noble houses that can trace themselves back to the Anglo-Saxons, especially after William the Conqueror’s Scouring of the North, and I don’t know any that can trace back to pre-Saxon times (although you might find Welsh noble houses that could do so). 

And keep in mind, that was a few hundred years of history. Westerosi houses can trace their lineages back by as much as eight thousand years.