It uses macaroni, so obviously it came about after pasta was introduced into England.
Recipes for Stokenchurch Pie just call for “cooked meat”, so it was a way to use up leftover meat of any kind that the householder might happen to have on hand.
To make the pie, you line an ovenproof dish with pastry, make a layer of cooked macaroni mixed with the cooked meat chopped up, then put in whole, peeled hard-boiled eggs, make a final layer of the macaroni and meat, then cover with pastry, make a hole in the top, then bake.
“Stokenchurch” is an old village in Buckinghamshire. Its name means “church made from logs.”