Two goals is not a lot. But when I looked it up I was surprised how many teams have done that (come out successfully from the preliminary round with only two goals) before the English, among them Ireland, Northern Ireland and Wales.

But the undisputed leader in this discipline (coming through with least goals and effort) is Italy. In 1982, they finished second in the preliminary round with no win and only two goals. In 1970, they even won their preliminary group with one single goal. They went on to win the final, later.

Wolfgang