I would have thought that for two teams to be proper rivals, they need to be almost equally as good as each other - Argentina and Germany are much better than England, they probably see England just like any other team, considering Holland and Brazil to be more worthy rivals. The problem with England is that they thing too much of themselves. If they beat a team, they consider that team to be beneath them. But if they get beaten by a team, they consider that team to be one of their rivals, when in reality, that team is far superior to England.
So on that basis, I would say that England's biggest rivals of late have been Croatia.