England did play Poland at Wembley and beat them 2-0 to qualify for the World Cup in Brazil in 2014. However, England in the film did better than the team in 2014 who went out in the group stage.
During the film it shows that English F.A. is based at Lancaster Gate, they moved away to Soho Square several months ago during the filming, and Wembley Stadium has been shut down for almost 7 month's upon the release of the film.
During the second secret interview with the dissident players, one of them claims that some players are "checking to see if they have Irish grandparents, to jump ship". However, FIFA rules do not allow a player to change national team once he has played an international game.
La Bombonera stadium (Estadio Alberto J. Armando), where the game against Mexico is placed, is located in Buenos Aires, Argentina, not Brazil. It's owned by Boca Juniors.