The name is known in England at least since 1637 (OED) and may derive from the Italian polpettone, a type of stuffed meatloaf. In the English version the loaf has shrunk to a crust and the filling expanded from the few simple vegetables of the original.
Benjamin Disraeli's novel Venetia has a meal ending with "a pompetone of larks".
"What a lark!"
From 'Punch', 1891
Original Receipt in 'English Housewifry' by Elizabeth Moxon, 1764 (Moxon 1764)146. To make a PALPATOON of PIGEONS.
Take mushrooms, pallets, oysters and sweet-breads, fry them in butter, put all these in a strong gravy, heat them over the fire, and thicken them up with an egg and a little butter; then take six or eight pigeons, truss them as you would for baking, season them with pepper and salt, and lay on them a crust of forc'd-meat as follows, viz. a pound of veal cut in little bits, and a pound and a half of marrow, beat it together in a stone mortar, after it is beat very fine, season it with mace, pepper and salt, put in the yolks of four eggs, and two raw eggs, mix altogether with a few bread crumbs to a paste: make the sides and lid of your pie with it, then put your ragoo into your dish, and lay in your pigeons with butter; an hour and a half will bake it.