The problem isn't keeping the birds (or any 'exotic' pet for that matter) so much as lack of correct knowledge passed on by many who sell such animals.
I know this from previously owning a 'rescued' Green Iguana. Few pet shops, and even more worryingly fewer vets new the correct husbandry techniques involved with such animals and hence a great deal of animals have suffered in the past.
You know I found only two vetenary practices near to me (well within 25 miles at least!) who I considered knowledgeable enough to treat the Iggs,, and when you consider the vast numbers of these animals sold I guess I could be forgiven for thinking it would be a good idea to outlaw such animals as pets. I don't though.
TBH I think to outlaw caged birds is ludicrous like someone has already pointed out it would be fishing and dogs next (actually I could live with that
).
This government don't need encorougment with any more ill though out authoritarian idea's in my opinion!
I would also recomend you give the petitions website a wide birth too, it's more Labour spin and only serves to make us all feel like the government listens to public opinion, but you see it is not the job of the government to listen to it's people anyway, after all we apoint the PM to make the 'best' decisions on our behalf, thats how it has always worked and how it always will work.