That seems unlikely, as there was also a cheese-based dish called English rabbit (and one called Scotch rabbit, for that matter):
To make a Scotch rabbit, toast the bread very nicely on both sides, butter it, cut a slice of cheese about as big as the bread, toast it on both sides, and lay it on the bread.
To make a Welsh rabbit, toast the bread on both sides, then toast the cheese on one side, lay it on the toast, and with a hot iron brown the other side. You may rub it over with mustard.
To make an English rabbit, toast the bread brown on both sides, lay it in a plate before the fire, pour a glass of red wine over it, and let it soak the wine up. Then cut some cheese very thin and lay it very thick over the bread, put it in a tin oven before the fire, and it will be toasted and browned presently. Serve it away hot.
