Parody isn't protectedin the UK
It never has been.
Parody is different from satire, I can say that the prime minister is an upper class toff who might be slightly out of touch with being unemployed in Barnsley - that's satire (crap satire but it should get me on channel 4)
Parody is a Weird Al Yankovic song or a lego reproduction of star wars. This is more protected in the US, but even then re-using an entire song with new lyrics or remaking a fan version of entire movie isn't protected.
Otherwise there would be no point in being a song writer - since everybody else's version of a Beatles song would be "a parody" and I wouldn't have to pay Lennon+McCartney anything when I got to number one.
What I can do in the US is print a picture of Rumsfeld as the Emperor from Star wars - that's both parody and satire and is protected.