The Motion Picture Association of America has agreed to give the awards contender a more family-friendly PG-13 rating.
The decision to change the rating came after Dench appeared as her James Bond film franchise character M and dispatched Coogan's Secret Agent 002 to Los Angeles to talk MPAA in a satirical Funny or Die video.
"We owe this victory to Barbara Broccoli, producer of the James Bond series, Daniel Craig and Sam Mendes who -- because of their relationship with Judi Dench -- gave permission to spoof the ratings system using the M character," TWC Co-Chairman Harvey Weinstein said in a statement Wednesday.
"We know that went a long way into shedding light on the themes of the movie and the fact that the PG-13 rating was correct. We are glad the MPAA has a good sense of humor and with the cooperation of Barbara and her team it was proven once again no one does it better than James Bond. And my sincerest congratulations to Steve Coogan, who went to the MPAA and defended the case personally."
"This is a film that evokes an overwhelmingly positive response from people," Frears said. "I'm delighted children have already seen it and have responded to it so positively.
"We felt the MPAA had made the wrong decision in handing the film, which has no violence or lewd material and the bare minimum of adult language, an R rating. I am overjoyed they've changed their ruling in order to give families like mine an opportunity to see this film together. Now we can let the whole world see it."