> Wouldn't an English pie be similar to something like "torta pasqualina"?
Nope, nothing like that, I think. English pies use thicker pastry, are filled with gravy and never anything green. Something like this[1] gives you an idea. Perhaps it's the sort of equivalent, but the Italian I work with says there is nothing like them that he's ever had in Italy.
1. http://www.bbcgoodfood.com/recipes/3148692/dads-beef-mushroo...