Again no. England weren't counter attacking.
Man United have won championships with a 4-4-2 and didn't counter attack.
Firstly, counter-attacking is inherent in being actively defensive. It's the other side of the coin and the reason it exists. England weren't counter-attacking because they didn't mean to be defensive, but because this formation, executed rigidly, cannot compete on the front foot in modern football.
Secondly, United last played real 4-4-2 in the year 2000 and Ferguson brought in Queiroz to stop it (in fact, Ferguson claims to have never actually played 4-4-2, but to have ini fact invented 4-2-3-1). Also, of course they counter-attacked, they were famous for it, but not in 4-4-2 and not for whole games.