Can't see that shooting them will do any good except give you a bit of target practice (are you sure this isn't the main attraction?) as the nest will still be occupied and producing young.
Most local authorities will sort out a rat infestation for free (not mice though).
Be very careful with a rifle - with the powers they have under our Anti-terrorist Laws you'll have armed police shooting back before you can say "Pied Piper of Hamelin".
I have bird friendly plants too Woofgang! I sometimes thing I should stop feeding them as well, but to be honest the rats are all round us anyway regardless of bird feeders.
We have a couple Tambo and have caught a couple of rats, but don't find them that good. We also caught the same robin twice!! We did set him free but he would have frozen to death if he had been left overnight in there.